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from __future__ import division, print_function, absolute_import
import numpy as np
from numpy.testing import (run_module_suite, assert_equal, assert_array_equal,
assert_array_almost_equal, assert_approx_equal, assert_raises,
assert_allclose)
from scipy.special import xlogy
from scipy.stats.contingency import margins, expected_freq, chi2_contingency
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)
def test_chi2_contingency_trivial():
# 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():
# 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():
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():
# 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)
if __name__ == "__main__":
run_module_suite()
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