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import numpy as np
from numpy.testing import (assert_equal, assert_array_equal,
assert_array_almost_equal, assert_approx_equal,
assert_allclose)
import pytest
from pytest import raises as assert_raises
from scipy import stats
from scipy.special import xlogy
from scipy.stats.contingency import (margins, expected_freq,
chi2_contingency, association)
def test_margins():
a = np.array([1])
m = margins(a)
assert_equal(len(m), 1)
m0 = m[0]
assert_array_equal(m0, np.array([1]))
a = np.array([[1]])
m0, m1 = margins(a)
expected0 = np.array([[1]])
expected1 = np.array([[1]])
assert_array_equal(m0, expected0)
assert_array_equal(m1, expected1)
a = np.arange(12).reshape(2, 6)
m0, m1 = margins(a)
expected0 = np.array([[15], [51]])
expected1 = np.array([[6, 8, 10, 12, 14, 16]])
assert_array_equal(m0, expected0)
assert_array_equal(m1, expected1)
a = np.arange(24).reshape(2, 3, 4)
m0, m1, m2 = margins(a)
expected0 = np.array([[[66]], [[210]]])
expected1 = np.array([[[60], [92], [124]]])
expected2 = np.array([[[60, 66, 72, 78]]])
assert_array_equal(m0, expected0)
assert_array_equal(m1, expected1)
assert_array_equal(m2, expected2)
def test_expected_freq():
assert_array_equal(expected_freq([1]), np.array([1.0]))
observed = np.array([[[2, 0], [0, 2]], [[0, 2], [2, 0]], [[1, 1], [1, 1]]])
e = expected_freq(observed)
assert_array_equal(e, np.ones_like(observed))
observed = np.array([[10, 10, 20], [20, 20, 20]])
e = expected_freq(observed)
correct = np.array([[12., 12., 16.], [18., 18., 24.]])
assert_array_almost_equal(e, correct)
class TestChi2Contingency:
def test_chi2_contingency_trivial(self):
# Some very simple tests for chi2_contingency.
# A trivial case
obs = np.array([[1, 2], [1, 2]])
chi2, p, dof, expected = chi2_contingency(obs, correction=False)
assert_equal(chi2, 0.0)
assert_equal(p, 1.0)
assert_equal(dof, 1)
assert_array_equal(obs, expected)
# A *really* trivial case: 1-D data.
obs = np.array([1, 2, 3])
chi2, p, dof, expected = chi2_contingency(obs, correction=False)
assert_equal(chi2, 0.0)
assert_equal(p, 1.0)
assert_equal(dof, 0)
assert_array_equal(obs, expected)
def test_chi2_contingency_R(self):
# Some test cases that were computed independently, using R.
# Rcode = \
# """
# # Data vector.
# data <- c(
# 12, 34, 23, 4, 47, 11,
# 35, 31, 11, 34, 10, 18,
# 12, 32, 9, 18, 13, 19,
# 12, 12, 14, 9, 33, 25
# )
#
# # Create factor tags:r=rows, c=columns, t=tiers
# r <- factor(gl(4, 2*3, 2*3*4, labels=c("r1", "r2", "r3", "r4")))
# c <- factor(gl(3, 1, 2*3*4, labels=c("c1", "c2", "c3")))
# t <- factor(gl(2, 3, 2*3*4, labels=c("t1", "t2")))
#
# # 3-way Chi squared test of independence
# s = summary(xtabs(data~r+c+t))
# print(s)
# """
# Routput = \
# """
# Call: xtabs(formula = data ~ r + c + t)
# Number of cases in table: 478
# Number of factors: 3
# Test for independence of all factors:
# Chisq = 102.17, df = 17, p-value = 3.514e-14
# """
obs = np.array(
[[[12, 34, 23],
[35, 31, 11],
[12, 32, 9],
[12, 12, 14]],
[[4, 47, 11],
[34, 10, 18],
[18, 13, 19],
[9, 33, 25]]])
chi2, p, dof, expected = chi2_contingency(obs)
assert_approx_equal(chi2, 102.17, significant=5)
assert_approx_equal(p, 3.514e-14, significant=4)
assert_equal(dof, 17)
# Rcode = \
# """
# # Data vector.
# data <- c(
# #
# 12, 17,
# 11, 16,
# #
# 11, 12,
# 15, 16,
# #
# 23, 15,
# 30, 22,
# #
# 14, 17,
# 15, 16
# )
#
# # Create factor tags:r=rows, c=columns, d=depths(?), t=tiers
# r <- factor(gl(2, 2, 2*2*2*2, labels=c("r1", "r2")))
# c <- factor(gl(2, 1, 2*2*2*2, labels=c("c1", "c2")))
# d <- factor(gl(2, 4, 2*2*2*2, labels=c("d1", "d2")))
# t <- factor(gl(2, 8, 2*2*2*2, labels=c("t1", "t2")))
#
# # 4-way Chi squared test of independence
# s = summary(xtabs(data~r+c+d+t))
# print(s)
# """
# Routput = \
# """
# Call: xtabs(formula = data ~ r + c + d + t)
# Number of cases in table: 262
# Number of factors: 4
# Test for independence of all factors:
# Chisq = 8.758, df = 11, p-value = 0.6442
# """
obs = np.array(
[[[[12, 17],
[11, 16]],
[[11, 12],
[15, 16]]],
[[[23, 15],
[30, 22]],
[[14, 17],
[15, 16]]]])
chi2, p, dof, expected = chi2_contingency(obs)
assert_approx_equal(chi2, 8.758, significant=4)
assert_approx_equal(p, 0.6442, significant=4)
assert_equal(dof, 11)
def test_chi2_contingency_g(self):
c = np.array([[15, 60], [15, 90]])
g, p, dof, e = chi2_contingency(c, lambda_='log-likelihood',
correction=False)
assert_allclose(g, 2*xlogy(c, c/e).sum())
g, p, dof, e = chi2_contingency(c, lambda_='log-likelihood',
correction=True)
c_corr = c + np.array([[-0.5, 0.5], [0.5, -0.5]])
assert_allclose(g, 2*xlogy(c_corr, c_corr/e).sum())
c = np.array([[10, 12, 10], [12, 10, 10]])
g, p, dof, e = chi2_contingency(c, lambda_='log-likelihood')
assert_allclose(g, 2*xlogy(c, c/e).sum())
def test_chi2_contingency_bad_args(self):
# Test that "bad" inputs raise a ValueError.
# Negative value in the array of observed frequencies.
obs = np.array([[-1, 10], [1, 2]])
assert_raises(ValueError, chi2_contingency, obs)
# The zeros in this will result in zeros in the array
# of expected frequencies.
obs = np.array([[0, 1], [0, 1]])
assert_raises(ValueError, chi2_contingency, obs)
# A degenerate case: `observed` has size 0.
obs = np.empty((0, 8))
assert_raises(ValueError, chi2_contingency, obs)
def test_chi2_contingency_yates_gh13875(self):
# Magnitude of Yates' continuity correction should not exceed difference
# between expected and observed value of the statistic; see gh-13875
observed = np.array([[1573, 3], [4, 0]])
p = chi2_contingency(observed)[1]
assert_allclose(p, 1, rtol=1e-12)
@pytest.mark.parametrize("correction", [False, True])
def test_result(self, correction):
obs = np.array([[1, 2], [1, 2]])
res = chi2_contingency(obs, correction=correction)
assert_equal((res.statistic, res.pvalue, res.dof, res.expected_freq), res)
@pytest.mark.slow
def test_exact_permutation(self):
table = np.arange(4).reshape(2, 2)
ref_statistic = chi2_contingency(table, correction=False).statistic
ref_pvalue = stats.fisher_exact(table).pvalue
method = stats.PermutationMethod(n_resamples=50000)
res = chi2_contingency(table, correction=False, method=method)
assert_equal(res.statistic, ref_statistic)
assert_allclose(res.pvalue, ref_pvalue, rtol=1e-15)
@pytest.mark.slow
@pytest.mark.parametrize('method', (stats.PermutationMethod,
stats.MonteCarloMethod))
def test_resampling_randomized(self, method):
rng = np.random.default_rng(2592340925)
# need to have big sum for asymptotic approximation to be good
rows = [300, 1000, 800]
cols = [200, 400, 800, 700]
table = stats.random_table(rows, cols, seed=rng).rvs()
res = chi2_contingency(table, correction=False, method=method(rng=rng))
ref = chi2_contingency(table, correction=False)
assert_equal(res.statistic, ref.statistic)
assert_allclose(res.pvalue, ref.pvalue, atol=5e-3)
assert_equal(res.dof, np.nan)
assert_equal(res.expected_freq, ref.expected_freq)
def test_resampling_invalid_args(self):
table = np.arange(8).reshape(2, 2, 2)
method = stats.PermutationMethod()
message = "Use of `method` is only compatible with two-way tables."
with pytest.raises(ValueError, match=message):
chi2_contingency(table, correction=False, method=method)
table = np.arange(4).reshape(2, 2)
method = stats.PermutationMethod()
message = "`correction=True` is not compatible with..."
with pytest.raises(ValueError, match=message):
chi2_contingency(table, method=method)
method = stats.MonteCarloMethod()
message = "`lambda_=2` is not compatible with..."
with pytest.raises(ValueError, match=message):
chi2_contingency(table, correction=False, lambda_=2, method=method)
method = 'herring'
message = "`method='herring'` not recognized; if provided, `method`..."
with pytest.raises(ValueError, match=message):
chi2_contingency(table, correction=False, method=method)
method = stats.MonteCarloMethod(rvs=stats.norm.rvs)
message = "If the `method` argument of `chi2_contingency` is..."
with pytest.raises(ValueError, match=message):
chi2_contingency(table, correction=False, method=method)
def test_bad_association_args():
# Invalid Test Statistic
assert_raises(ValueError, association, [[1, 2], [3, 4]], "X")
# Invalid array shape
assert_raises(ValueError, association, [[[1, 2]], [[3, 4]]], "cramer")
# chi2_contingency exception
assert_raises(ValueError, association, [[-1, 10], [1, 2]], 'cramer')
# Invalid Array Item Data Type
assert_raises(ValueError, association,
np.array([[1, 2], ["dd", 4]], dtype=object), 'cramer')
@pytest.mark.parametrize('stat, expected',
[('cramer', 0.09222412010290792),
('tschuprow', 0.0775509319944633),
('pearson', 0.12932925727138758)])
def test_assoc(stat, expected):
# 2d Array
obs1 = np.array([[12, 13, 14, 15, 16],
[17, 16, 18, 19, 11],
[9, 15, 14, 12, 11]])
a = association(observed=obs1, method=stat)
assert_allclose(a, expected)
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