1858 lines
78 KiB
Python
1858 lines
78 KiB
Python
from itertools import product
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import numpy as np
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import random
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import functools
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import pytest
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from numpy.testing import (assert_, assert_equal, assert_allclose,
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assert_almost_equal) # avoid new uses
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from pytest import raises as assert_raises
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import scipy.stats as stats
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from scipy.stats import distributions
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from scipy.stats._hypotests import (epps_singleton_2samp, cramervonmises,
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_cdf_cvm, cramervonmises_2samp,
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_pval_cvm_2samp_exact, barnard_exact,
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boschloo_exact)
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from scipy.stats._mannwhitneyu import mannwhitneyu, _mwu_state
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from .common_tests import check_named_results
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from scipy._lib._testutils import _TestPythranFunc
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from scipy.stats._axis_nan_policy import SmallSampleWarning, too_small_1d_not_omit
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class TestEppsSingleton:
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def test_statistic_1(self):
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# first example in Goerg & Kaiser, also in original paper of
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# Epps & Singleton. Note: values do not match exactly, the
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# value of the interquartile range varies depending on how
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# quantiles are computed
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x = np.array([-0.35, 2.55, 1.73, 0.73, 0.35,
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2.69, 0.46, -0.94, -0.37, 12.07])
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y = np.array([-1.15, -0.15, 2.48, 3.25, 3.71,
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4.29, 5.00, 7.74, 8.38, 8.60])
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w, p = epps_singleton_2samp(x, y)
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assert_almost_equal(w, 15.14, decimal=1)
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assert_almost_equal(p, 0.00442, decimal=3)
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def test_statistic_2(self):
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# second example in Goerg & Kaiser, again not a perfect match
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x = np.array((0, 1, 2, 2, 2, 2, 3, 3, 3, 3, 4, 5, 5, 5, 5, 6, 10,
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10, 10, 10))
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y = np.array((10, 4, 0, 5, 10, 10, 0, 5, 6, 7, 10, 3, 1, 7, 0, 8, 1,
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5, 8, 10))
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w, p = epps_singleton_2samp(x, y)
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assert_allclose(w, 8.900, atol=0.001)
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assert_almost_equal(p, 0.06364, decimal=3)
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def test_epps_singleton_array_like(self):
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np.random.seed(1234)
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x, y = np.arange(30), np.arange(28)
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w1, p1 = epps_singleton_2samp(list(x), list(y))
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w2, p2 = epps_singleton_2samp(tuple(x), tuple(y))
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w3, p3 = epps_singleton_2samp(x, y)
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assert_(w1 == w2 == w3)
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assert_(p1 == p2 == p3)
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def test_epps_singleton_size(self):
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# warns if sample contains fewer than 5 elements
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x, y = (1, 2, 3, 4), np.arange(10)
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with pytest.warns(SmallSampleWarning, match=too_small_1d_not_omit):
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res = epps_singleton_2samp(x, y)
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assert_equal(res.statistic, np.nan)
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assert_equal(res.pvalue, np.nan)
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def test_epps_singleton_nonfinite(self):
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# raise error if there are non-finite values
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x, y = (1, 2, 3, 4, 5, np.inf), np.arange(10)
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assert_raises(ValueError, epps_singleton_2samp, x, y)
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def test_names(self):
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x, y = np.arange(20), np.arange(30)
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res = epps_singleton_2samp(x, y)
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attributes = ('statistic', 'pvalue')
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check_named_results(res, attributes)
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class TestCvm:
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# the expected values of the cdfs are taken from Table 1 in
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# Csorgo / Faraway: The Exact and Asymptotic Distribution of
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# Cramér-von Mises Statistics, 1996.
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def test_cdf_4(self):
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assert_allclose(
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_cdf_cvm([0.02983, 0.04111, 0.12331, 0.94251], 4),
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[0.01, 0.05, 0.5, 0.999],
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atol=1e-4)
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def test_cdf_10(self):
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assert_allclose(
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_cdf_cvm([0.02657, 0.03830, 0.12068, 0.56643], 10),
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[0.01, 0.05, 0.5, 0.975],
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atol=1e-4)
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def test_cdf_1000(self):
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assert_allclose(
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_cdf_cvm([0.02481, 0.03658, 0.11889, 1.16120], 1000),
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[0.01, 0.05, 0.5, 0.999],
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atol=1e-4)
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def test_cdf_inf(self):
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assert_allclose(
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_cdf_cvm([0.02480, 0.03656, 0.11888, 1.16204]),
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[0.01, 0.05, 0.5, 0.999],
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atol=1e-4)
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def test_cdf_support(self):
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# cdf has support on [1/(12*n), n/3]
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assert_equal(_cdf_cvm([1/(12*533), 533/3], 533), [0, 1])
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assert_equal(_cdf_cvm([1/(12*(27 + 1)), (27 + 1)/3], 27), [0, 1])
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def test_cdf_large_n(self):
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# test that asymptotic cdf and cdf for large samples are close
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assert_allclose(
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_cdf_cvm([0.02480, 0.03656, 0.11888, 1.16204, 100], 10000),
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_cdf_cvm([0.02480, 0.03656, 0.11888, 1.16204, 100]),
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atol=1e-4)
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def test_large_x(self):
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# for large values of x and n, the series used to compute the cdf
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# converges slowly.
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# this leads to bug in R package goftest and MAPLE code that is
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# the basis of the implementation in scipy
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# note: cdf = 1 for x >= 1000/3 and n = 1000
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assert_(0.99999 < _cdf_cvm(333.3, 1000) < 1.0)
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assert_(0.99999 < _cdf_cvm(333.3) < 1.0)
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def test_low_p(self):
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# _cdf_cvm can return values larger than 1. In that case, we just
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# return a p-value of zero.
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n = 12
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res = cramervonmises(np.ones(n)*0.8, 'norm')
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assert_(_cdf_cvm(res.statistic, n) > 1.0)
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assert_equal(res.pvalue, 0)
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@pytest.mark.parametrize('x', [(), [1.5]])
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def test_invalid_input(self, x):
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with pytest.warns(SmallSampleWarning, match=too_small_1d_not_omit):
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res = cramervonmises(x, "norm")
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assert_equal(res.statistic, np.nan)
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assert_equal(res.pvalue, np.nan)
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def test_values_R(self):
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# compared against R package goftest, version 1.1.1
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# goftest::cvm.test(c(-1.7, 2, 0, 1.3, 4, 0.1, 0.6), "pnorm")
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res = cramervonmises([-1.7, 2, 0, 1.3, 4, 0.1, 0.6], "norm")
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assert_allclose(res.statistic, 0.288156, atol=1e-6)
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assert_allclose(res.pvalue, 0.1453465, atol=1e-6)
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# goftest::cvm.test(c(-1.7, 2, 0, 1.3, 4, 0.1, 0.6),
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# "pnorm", mean = 3, sd = 1.5)
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res = cramervonmises([-1.7, 2, 0, 1.3, 4, 0.1, 0.6], "norm", (3, 1.5))
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assert_allclose(res.statistic, 0.9426685, atol=1e-6)
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assert_allclose(res.pvalue, 0.002026417, atol=1e-6)
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# goftest::cvm.test(c(1, 2, 5, 1.4, 0.14, 11, 13, 0.9, 7.5), "pexp")
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res = cramervonmises([1, 2, 5, 1.4, 0.14, 11, 13, 0.9, 7.5], "expon")
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assert_allclose(res.statistic, 0.8421854, atol=1e-6)
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assert_allclose(res.pvalue, 0.004433406, atol=1e-6)
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def test_callable_cdf(self):
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x, args = np.arange(5), (1.4, 0.7)
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r1 = cramervonmises(x, distributions.expon.cdf)
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r2 = cramervonmises(x, "expon")
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assert_equal((r1.statistic, r1.pvalue), (r2.statistic, r2.pvalue))
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r1 = cramervonmises(x, distributions.beta.cdf, args)
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r2 = cramervonmises(x, "beta", args)
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assert_equal((r1.statistic, r1.pvalue), (r2.statistic, r2.pvalue))
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class TestMannWhitneyU:
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# All magic numbers are from R wilcox.test unless otherwise specified
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# https://rdrr.io/r/stats/wilcox.test.html
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# --- Test Input Validation ---
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@pytest.mark.parametrize('kwargs_update', [{'x': []}, {'y': []},
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{'x': [], 'y': []}])
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def test_empty(self, kwargs_update):
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x = np.array([1, 2]) # generic, valid inputs
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y = np.array([3, 4])
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kwargs = dict(x=x, y=y)
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kwargs.update(kwargs_update)
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with pytest.warns(SmallSampleWarning, match=too_small_1d_not_omit):
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res = mannwhitneyu(**kwargs)
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assert_equal(res.statistic, np.nan)
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assert_equal(res.pvalue, np.nan)
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def test_input_validation(self):
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x = np.array([1, 2]) # generic, valid inputs
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y = np.array([3, 4])
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with assert_raises(ValueError, match="`use_continuity` must be one"):
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mannwhitneyu(x, y, use_continuity='ekki')
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with assert_raises(ValueError, match="`alternative` must be one of"):
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mannwhitneyu(x, y, alternative='ekki')
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with assert_raises(ValueError, match="`axis` must be an integer"):
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mannwhitneyu(x, y, axis=1.5)
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with assert_raises(ValueError, match="`method` must be one of"):
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mannwhitneyu(x, y, method='ekki')
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def test_auto(self):
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# Test that default method ('auto') chooses intended method
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np.random.seed(1)
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n = 8 # threshold to switch from exact to asymptotic
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# both inputs are smaller than threshold; should use exact
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x = np.random.rand(n-1)
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y = np.random.rand(n-1)
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auto = mannwhitneyu(x, y)
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asymptotic = mannwhitneyu(x, y, method='asymptotic')
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exact = mannwhitneyu(x, y, method='exact')
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assert auto.pvalue == exact.pvalue
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assert auto.pvalue != asymptotic.pvalue
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# one input is smaller than threshold; should use exact
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x = np.random.rand(n-1)
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y = np.random.rand(n+1)
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auto = mannwhitneyu(x, y)
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asymptotic = mannwhitneyu(x, y, method='asymptotic')
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exact = mannwhitneyu(x, y, method='exact')
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assert auto.pvalue == exact.pvalue
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assert auto.pvalue != asymptotic.pvalue
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# other input is smaller than threshold; should use exact
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auto = mannwhitneyu(y, x)
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asymptotic = mannwhitneyu(x, y, method='asymptotic')
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exact = mannwhitneyu(x, y, method='exact')
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assert auto.pvalue == exact.pvalue
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assert auto.pvalue != asymptotic.pvalue
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# both inputs are larger than threshold; should use asymptotic
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x = np.random.rand(n+1)
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y = np.random.rand(n+1)
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auto = mannwhitneyu(x, y)
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asymptotic = mannwhitneyu(x, y, method='asymptotic')
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exact = mannwhitneyu(x, y, method='exact')
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assert auto.pvalue != exact.pvalue
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assert auto.pvalue == asymptotic.pvalue
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# both inputs are smaller than threshold, but there is a tie
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# should use asymptotic
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x = np.random.rand(n-1)
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y = np.random.rand(n-1)
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y[3] = x[3]
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auto = mannwhitneyu(x, y)
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asymptotic = mannwhitneyu(x, y, method='asymptotic')
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exact = mannwhitneyu(x, y, method='exact')
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assert auto.pvalue != exact.pvalue
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assert auto.pvalue == asymptotic.pvalue
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# --- Test Basic Functionality ---
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x = [210.052110, 110.190630, 307.918612]
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y = [436.08811482466416, 416.37397329768191, 179.96975939463582,
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197.8118754228619, 34.038757281225756, 138.54220550921517,
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128.7769351470246, 265.92721427951852, 275.6617533155341,
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592.34083395416258, 448.73177590617018, 300.61495185038905,
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187.97508449019588]
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# This test was written for mann_whitney_u in gh-4933.
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# Originally, the p-values for alternatives were swapped;
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# this has been corrected and the tests have been refactored for
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# compactness, but otherwise the tests are unchanged.
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# R code for comparison, e.g.:
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# options(digits = 16)
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# x = c(210.052110, 110.190630, 307.918612)
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# y = c(436.08811482466416, 416.37397329768191, 179.96975939463582,
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# 197.8118754228619, 34.038757281225756, 138.54220550921517,
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# 128.7769351470246, 265.92721427951852, 275.6617533155341,
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# 592.34083395416258, 448.73177590617018, 300.61495185038905,
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# 187.97508449019588)
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# wilcox.test(x, y, alternative="g", exact=TRUE)
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cases_basic = [[{"alternative": 'two-sided', "method": "asymptotic"},
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(16, 0.6865041817876)],
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[{"alternative": 'less', "method": "asymptotic"},
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(16, 0.3432520908938)],
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[{"alternative": 'greater', "method": "asymptotic"},
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(16, 0.7047591913255)],
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[{"alternative": 'two-sided', "method": "exact"},
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(16, 0.7035714285714)],
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[{"alternative": 'less', "method": "exact"},
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(16, 0.3517857142857)],
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[{"alternative": 'greater', "method": "exact"},
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(16, 0.6946428571429)]]
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@pytest.mark.parametrize(("kwds", "expected"), cases_basic)
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def test_basic(self, kwds, expected):
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res = mannwhitneyu(self.x, self.y, **kwds)
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assert_allclose(res, expected)
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cases_continuity = [[{"alternative": 'two-sided', "use_continuity": True},
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(23, 0.6865041817876)],
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[{"alternative": 'less', "use_continuity": True},
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(23, 0.7047591913255)],
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[{"alternative": 'greater', "use_continuity": True},
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(23, 0.3432520908938)],
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[{"alternative": 'two-sided', "use_continuity": False},
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(23, 0.6377328900502)],
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[{"alternative": 'less', "use_continuity": False},
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(23, 0.6811335549749)],
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[{"alternative": 'greater', "use_continuity": False},
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(23, 0.3188664450251)]]
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@pytest.mark.parametrize(("kwds", "expected"), cases_continuity)
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def test_continuity(self, kwds, expected):
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# When x and y are interchanged, less and greater p-values should
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# swap (compare to above). This wouldn't happen if the continuity
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# correction were applied in the wrong direction. Note that less and
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# greater p-values do not sum to 1 when continuity correction is on,
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# which is what we'd expect. Also check that results match R when
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# continuity correction is turned off.
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# Note that method='asymptotic' -> exact=FALSE
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# and use_continuity=False -> correct=FALSE, e.g.:
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# wilcox.test(x, y, alternative="t", exact=FALSE, correct=FALSE)
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res = mannwhitneyu(self.y, self.x, method='asymptotic', **kwds)
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assert_allclose(res, expected)
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def test_tie_correct(self):
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# Test tie correction against R's wilcox.test
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# options(digits = 16)
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# x = c(1, 2, 3, 4)
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# y = c(1, 2, 3, 4, 5)
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# wilcox.test(x, y, exact=FALSE)
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x = [1, 2, 3, 4]
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y0 = np.array([1, 2, 3, 4, 5])
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dy = np.array([0, 1, 0, 1, 0])*0.01
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dy2 = np.array([0, 0, 1, 0, 0])*0.01
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y = [y0-0.01, y0-dy, y0-dy2, y0, y0+dy2, y0+dy, y0+0.01]
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res = mannwhitneyu(x, y, axis=-1, method="asymptotic")
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U_expected = [10, 9, 8.5, 8, 7.5, 7, 6]
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p_expected = [1, 0.9017048037317, 0.804080657472, 0.7086240584439,
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0.6197963884941, 0.5368784563079, 0.3912672792826]
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assert_equal(res.statistic, U_expected)
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assert_allclose(res.pvalue, p_expected)
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# --- Test Exact Distribution of U ---
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# These are tabulated values of the CDF of the exact distribution of
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# the test statistic from pg 52 of reference [1] (Mann-Whitney Original)
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pn3 = {1: [0.25, 0.5, 0.75], 2: [0.1, 0.2, 0.4, 0.6],
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3: [0.05, .1, 0.2, 0.35, 0.5, 0.65]}
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pn4 = {1: [0.2, 0.4, 0.6], 2: [0.067, 0.133, 0.267, 0.4, 0.6],
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3: [0.028, 0.057, 0.114, 0.2, .314, 0.429, 0.571],
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4: [0.014, 0.029, 0.057, 0.1, 0.171, 0.243, 0.343, 0.443, 0.557]}
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pm5 = {1: [0.167, 0.333, 0.5, 0.667],
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2: [0.047, 0.095, 0.19, 0.286, 0.429, 0.571],
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3: [0.018, 0.036, 0.071, 0.125, 0.196, 0.286, 0.393, 0.5, 0.607],
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4: [0.008, 0.016, 0.032, 0.056, 0.095, 0.143,
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0.206, 0.278, 0.365, 0.452, 0.548],
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5: [0.004, 0.008, 0.016, 0.028, 0.048, 0.075, 0.111,
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0.155, 0.21, 0.274, 0.345, .421, 0.5, 0.579]}
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pm6 = {1: [0.143, 0.286, 0.428, 0.571],
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2: [0.036, 0.071, 0.143, 0.214, 0.321, 0.429, 0.571],
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3: [0.012, 0.024, 0.048, 0.083, 0.131,
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0.19, 0.274, 0.357, 0.452, 0.548],
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4: [0.005, 0.01, 0.019, 0.033, 0.057, 0.086, 0.129,
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0.176, 0.238, 0.305, 0.381, 0.457, 0.543], # the last element
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# of the previous list, 0.543, has been modified from 0.545;
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# I assume it was a typo
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5: [0.002, 0.004, 0.009, 0.015, 0.026, 0.041, 0.063, 0.089,
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0.123, 0.165, 0.214, 0.268, 0.331, 0.396, 0.465, 0.535],
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6: [0.001, 0.002, 0.004, 0.008, 0.013, 0.021, 0.032, 0.047,
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0.066, 0.09, 0.12, 0.155, 0.197, 0.242, 0.294, 0.350,
|
|
0.409, 0.469, 0.531]}
|
|
|
|
def test_exact_distribution(self):
|
|
# I considered parametrize. I decided against it.
|
|
p_tables = {3: self.pn3, 4: self.pn4, 5: self.pm5, 6: self.pm6}
|
|
for n, table in p_tables.items():
|
|
for m, p in table.items():
|
|
# check p-value against table
|
|
u = np.arange(0, len(p))
|
|
_mwu_state.set_shapes(m, n)
|
|
assert_allclose(_mwu_state.cdf(k=u), p, atol=1e-3)
|
|
|
|
# check identity CDF + SF - PMF = 1
|
|
# ( In this implementation, SF(U) includes PMF(U) )
|
|
u2 = np.arange(0, m*n+1)
|
|
assert_allclose(_mwu_state.cdf(k=u2)
|
|
+ _mwu_state.sf(k=u2)
|
|
- _mwu_state.pmf(k=u2), 1)
|
|
|
|
# check symmetry about mean of U, i.e. pmf(U) = pmf(m*n-U)
|
|
pmf = _mwu_state.pmf(k=u2)
|
|
assert_allclose(pmf, pmf[::-1])
|
|
|
|
# check symmetry w.r.t. interchange of m, n
|
|
_mwu_state.set_shapes(n, m)
|
|
pmf2 = _mwu_state.pmf(k=u2)
|
|
assert_allclose(pmf, pmf2)
|
|
|
|
def test_asymptotic_behavior(self):
|
|
np.random.seed(0)
|
|
|
|
# for small samples, the asymptotic test is not very accurate
|
|
x = np.random.rand(5)
|
|
y = np.random.rand(5)
|
|
res1 = mannwhitneyu(x, y, method="exact")
|
|
res2 = mannwhitneyu(x, y, method="asymptotic")
|
|
assert res1.statistic == res2.statistic
|
|
assert np.abs(res1.pvalue - res2.pvalue) > 1e-2
|
|
|
|
# for large samples, they agree reasonably well
|
|
x = np.random.rand(40)
|
|
y = np.random.rand(40)
|
|
res1 = mannwhitneyu(x, y, method="exact")
|
|
res2 = mannwhitneyu(x, y, method="asymptotic")
|
|
assert res1.statistic == res2.statistic
|
|
assert np.abs(res1.pvalue - res2.pvalue) < 1e-3
|
|
|
|
# --- Test Corner Cases ---
|
|
|
|
def test_exact_U_equals_mean(self):
|
|
# Test U == m*n/2 with exact method
|
|
# Without special treatment, two-sided p-value > 1 because both
|
|
# one-sided p-values are > 0.5
|
|
res_l = mannwhitneyu([1, 2, 3], [1.5, 2.5], alternative="less",
|
|
method="exact")
|
|
res_g = mannwhitneyu([1, 2, 3], [1.5, 2.5], alternative="greater",
|
|
method="exact")
|
|
assert_equal(res_l.pvalue, res_g.pvalue)
|
|
assert res_l.pvalue > 0.5
|
|
|
|
res = mannwhitneyu([1, 2, 3], [1.5, 2.5], alternative="two-sided",
|
|
method="exact")
|
|
assert_equal(res, (3, 1))
|
|
# U == m*n/2 for asymptotic case tested in test_gh_2118
|
|
# The reason it's tricky for the asymptotic test has to do with
|
|
# continuity correction.
|
|
|
|
cases_scalar = [[{"alternative": 'two-sided', "method": "asymptotic"},
|
|
(0, 1)],
|
|
[{"alternative": 'less', "method": "asymptotic"},
|
|
(0, 0.5)],
|
|
[{"alternative": 'greater', "method": "asymptotic"},
|
|
(0, 0.977249868052)],
|
|
[{"alternative": 'two-sided', "method": "exact"}, (0, 1)],
|
|
[{"alternative": 'less', "method": "exact"}, (0, 0.5)],
|
|
[{"alternative": 'greater', "method": "exact"}, (0, 1)]]
|
|
|
|
@pytest.mark.parametrize(("kwds", "result"), cases_scalar)
|
|
def test_scalar_data(self, kwds, result):
|
|
# just making sure scalars work
|
|
assert_allclose(mannwhitneyu(1, 2, **kwds), result)
|
|
|
|
def test_equal_scalar_data(self):
|
|
# when two scalars are equal, there is an -0.5/0 in the asymptotic
|
|
# approximation. R gives pvalue=1.0 for alternatives 'less' and
|
|
# 'greater' but NA for 'two-sided'. I don't see why, so I don't
|
|
# see a need for a special case to match that behavior.
|
|
assert_equal(mannwhitneyu(1, 1, method="exact"), (0.5, 1))
|
|
assert_equal(mannwhitneyu(1, 1, method="asymptotic"), (0.5, 1))
|
|
|
|
# without continuity correction, this becomes 0/0, which really
|
|
# is undefined
|
|
assert_equal(mannwhitneyu(1, 1, method="asymptotic",
|
|
use_continuity=False), (0.5, np.nan))
|
|
|
|
# --- Test Enhancements / Bug Reports ---
|
|
|
|
@pytest.mark.parametrize("method", ["asymptotic", "exact"])
|
|
def test_gh_12837_11113(self, method):
|
|
# Test that behavior for broadcastable nd arrays is appropriate:
|
|
# output shape is correct and all values are equal to when the test
|
|
# is performed on one pair of samples at a time.
|
|
# Tests that gh-12837 and gh-11113 (requests for n-d input)
|
|
# are resolved
|
|
np.random.seed(0)
|
|
|
|
# arrays are broadcastable except for axis = -3
|
|
axis = -3
|
|
m, n = 7, 10 # sample sizes
|
|
x = np.random.rand(m, 3, 8)
|
|
y = np.random.rand(6, n, 1, 8) + 0.1
|
|
res = mannwhitneyu(x, y, method=method, axis=axis)
|
|
|
|
shape = (6, 3, 8) # appropriate shape of outputs, given inputs
|
|
assert res.pvalue.shape == shape
|
|
assert res.statistic.shape == shape
|
|
|
|
# move axis of test to end for simplicity
|
|
x, y = np.moveaxis(x, axis, -1), np.moveaxis(y, axis, -1)
|
|
|
|
x = x[None, ...] # give x a zeroth dimension
|
|
assert x.ndim == y.ndim
|
|
|
|
x = np.broadcast_to(x, shape + (m,))
|
|
y = np.broadcast_to(y, shape + (n,))
|
|
assert x.shape[:-1] == shape
|
|
assert y.shape[:-1] == shape
|
|
|
|
# loop over pairs of samples
|
|
statistics = np.zeros(shape)
|
|
pvalues = np.zeros(shape)
|
|
for indices in product(*[range(i) for i in shape]):
|
|
xi = x[indices]
|
|
yi = y[indices]
|
|
temp = mannwhitneyu(xi, yi, method=method)
|
|
statistics[indices] = temp.statistic
|
|
pvalues[indices] = temp.pvalue
|
|
|
|
np.testing.assert_equal(res.pvalue, pvalues)
|
|
np.testing.assert_equal(res.statistic, statistics)
|
|
|
|
def test_gh_11355(self):
|
|
# Test for correct behavior with NaN/Inf in input
|
|
x = [1, 2, 3, 4]
|
|
y = [3, 6, 7, 8, 9, 3, 2, 1, 4, 4, 5]
|
|
res1 = mannwhitneyu(x, y)
|
|
|
|
# Inf is not a problem. This is a rank test, and it's the largest value
|
|
y[4] = np.inf
|
|
res2 = mannwhitneyu(x, y)
|
|
|
|
assert_equal(res1.statistic, res2.statistic)
|
|
assert_equal(res1.pvalue, res2.pvalue)
|
|
|
|
# NaNs should propagate by default.
|
|
y[4] = np.nan
|
|
res3 = mannwhitneyu(x, y)
|
|
assert_equal(res3.statistic, np.nan)
|
|
assert_equal(res3.pvalue, np.nan)
|
|
|
|
cases_11355 = [([1, 2, 3, 4],
|
|
[3, 6, 7, 8, np.inf, 3, 2, 1, 4, 4, 5],
|
|
10, 0.1297704873477),
|
|
([1, 2, 3, 4],
|
|
[3, 6, 7, 8, np.inf, np.inf, 2, 1, 4, 4, 5],
|
|
8.5, 0.08735617507695),
|
|
([1, 2, np.inf, 4],
|
|
[3, 6, 7, 8, np.inf, 3, 2, 1, 4, 4, 5],
|
|
17.5, 0.5988856695752),
|
|
([1, 2, np.inf, 4],
|
|
[3, 6, 7, 8, np.inf, np.inf, 2, 1, 4, 4, 5],
|
|
16, 0.4687165824462),
|
|
([1, np.inf, np.inf, 4],
|
|
[3, 6, 7, 8, np.inf, np.inf, 2, 1, 4, 4, 5],
|
|
24.5, 0.7912517950119)]
|
|
|
|
@pytest.mark.parametrize(("x", "y", "statistic", "pvalue"), cases_11355)
|
|
def test_gh_11355b(self, x, y, statistic, pvalue):
|
|
# Test for correct behavior with NaN/Inf in input
|
|
res = mannwhitneyu(x, y, method='asymptotic')
|
|
assert_allclose(res.statistic, statistic, atol=1e-12)
|
|
assert_allclose(res.pvalue, pvalue, atol=1e-12)
|
|
|
|
cases_9184 = [[True, "less", "asymptotic", 0.900775348204],
|
|
[True, "greater", "asymptotic", 0.1223118025635],
|
|
[True, "two-sided", "asymptotic", 0.244623605127],
|
|
[False, "less", "asymptotic", 0.8896643190401],
|
|
[False, "greater", "asymptotic", 0.1103356809599],
|
|
[False, "two-sided", "asymptotic", 0.2206713619198],
|
|
[True, "less", "exact", 0.8967698967699],
|
|
[True, "greater", "exact", 0.1272061272061],
|
|
[True, "two-sided", "exact", 0.2544122544123]]
|
|
|
|
@pytest.mark.parametrize(("use_continuity", "alternative",
|
|
"method", "pvalue_exp"), cases_9184)
|
|
def test_gh_9184(self, use_continuity, alternative, method, pvalue_exp):
|
|
# gh-9184 might be considered a doc-only bug. Please see the
|
|
# documentation to confirm that mannwhitneyu correctly notes
|
|
# that the output statistic is that of the first sample (x). In any
|
|
# case, check the case provided there against output from R.
|
|
# R code:
|
|
# options(digits=16)
|
|
# x <- c(0.80, 0.83, 1.89, 1.04, 1.45, 1.38, 1.91, 1.64, 0.73, 1.46)
|
|
# y <- c(1.15, 0.88, 0.90, 0.74, 1.21)
|
|
# wilcox.test(x, y, alternative = "less", exact = FALSE)
|
|
# wilcox.test(x, y, alternative = "greater", exact = FALSE)
|
|
# wilcox.test(x, y, alternative = "two.sided", exact = FALSE)
|
|
# wilcox.test(x, y, alternative = "less", exact = FALSE,
|
|
# correct=FALSE)
|
|
# wilcox.test(x, y, alternative = "greater", exact = FALSE,
|
|
# correct=FALSE)
|
|
# wilcox.test(x, y, alternative = "two.sided", exact = FALSE,
|
|
# correct=FALSE)
|
|
# wilcox.test(x, y, alternative = "less", exact = TRUE)
|
|
# wilcox.test(x, y, alternative = "greater", exact = TRUE)
|
|
# wilcox.test(x, y, alternative = "two.sided", exact = TRUE)
|
|
statistic_exp = 35
|
|
x = (0.80, 0.83, 1.89, 1.04, 1.45, 1.38, 1.91, 1.64, 0.73, 1.46)
|
|
y = (1.15, 0.88, 0.90, 0.74, 1.21)
|
|
res = mannwhitneyu(x, y, use_continuity=use_continuity,
|
|
alternative=alternative, method=method)
|
|
assert_equal(res.statistic, statistic_exp)
|
|
assert_allclose(res.pvalue, pvalue_exp)
|
|
|
|
def test_gh_4067(self):
|
|
# Test for correct behavior with all NaN input - default is propagate
|
|
a = np.array([np.nan, np.nan, np.nan, np.nan, np.nan])
|
|
b = np.array([np.nan, np.nan, np.nan, np.nan, np.nan])
|
|
res = mannwhitneyu(a, b)
|
|
assert_equal(res.statistic, np.nan)
|
|
assert_equal(res.pvalue, np.nan)
|
|
|
|
# All cases checked against R wilcox.test, e.g.
|
|
# options(digits=16)
|
|
# x = c(1, 2, 3)
|
|
# y = c(1.5, 2.5)
|
|
# wilcox.test(x, y, exact=FALSE, alternative='less')
|
|
|
|
cases_2118 = [[[1, 2, 3], [1.5, 2.5], "greater", (3, 0.6135850036578)],
|
|
[[1, 2, 3], [1.5, 2.5], "less", (3, 0.6135850036578)],
|
|
[[1, 2, 3], [1.5, 2.5], "two-sided", (3, 1.0)],
|
|
[[1, 2, 3], [2], "greater", (1.5, 0.681324055883)],
|
|
[[1, 2, 3], [2], "less", (1.5, 0.681324055883)],
|
|
[[1, 2, 3], [2], "two-sided", (1.5, 1)],
|
|
[[1, 2], [1, 2], "greater", (2, 0.667497228949)],
|
|
[[1, 2], [1, 2], "less", (2, 0.667497228949)],
|
|
[[1, 2], [1, 2], "two-sided", (2, 1)]]
|
|
|
|
@pytest.mark.parametrize(["x", "y", "alternative", "expected"], cases_2118)
|
|
def test_gh_2118(self, x, y, alternative, expected):
|
|
# test cases in which U == m*n/2 when method is asymptotic
|
|
# applying continuity correction could result in p-value > 1
|
|
res = mannwhitneyu(x, y, use_continuity=True, alternative=alternative,
|
|
method="asymptotic")
|
|
assert_allclose(res, expected, rtol=1e-12)
|
|
|
|
def test_gh19692_smaller_table(self):
|
|
# In gh-19692, we noted that the shape of the cache used in calculating
|
|
# p-values was dependent on the order of the inputs because the sample
|
|
# sizes n1 and n2 changed. This was indicative of unnecessary cache
|
|
# growth and redundant calculation. Check that this is resolved.
|
|
rng = np.random.default_rng(7600451795963068007)
|
|
m, n = 5, 11
|
|
x = rng.random(size=m)
|
|
y = rng.random(size=n)
|
|
_mwu_state.reset() # reset cache
|
|
res = stats.mannwhitneyu(x, y, method='exact')
|
|
shape = _mwu_state.configurations.shape
|
|
assert shape[-1] == min(res.statistic, m*n - res.statistic) + 1
|
|
stats.mannwhitneyu(y, x, method='exact')
|
|
assert shape == _mwu_state.configurations.shape # same when sizes are reversed
|
|
|
|
# Also, we weren't exploiting the symmmetry of the null distribution
|
|
# to its full potential. Ensure that the null distribution is not
|
|
# evaluated explicitly for `k > m*n/2`.
|
|
_mwu_state.reset() # reset cache
|
|
stats.mannwhitneyu(x, 0*y, method='exact', alternative='greater')
|
|
shape = _mwu_state.configurations.shape
|
|
assert shape[-1] == 1 # k is smallest possible
|
|
stats.mannwhitneyu(0*x, y, method='exact', alternative='greater')
|
|
assert shape == _mwu_state.configurations.shape
|
|
|
|
@pytest.mark.parametrize('alternative', ['less', 'greater', 'two-sided'])
|
|
def test_permutation_method(self, alternative):
|
|
rng = np.random.default_rng(7600451795963068007)
|
|
x = rng.random(size=(2, 5))
|
|
y = rng.random(size=(2, 6))
|
|
res = stats.mannwhitneyu(x, y, method=stats.PermutationMethod(),
|
|
alternative=alternative, axis=1)
|
|
res2 = stats.mannwhitneyu(x, y, method='exact',
|
|
alternative=alternative, axis=1)
|
|
assert_allclose(res.statistic, res2.statistic, rtol=1e-15)
|
|
assert_allclose(res.pvalue, res2.pvalue, rtol=1e-15)
|
|
|
|
|
|
class TestSomersD(_TestPythranFunc):
|
|
def setup_method(self):
|
|
self.dtypes = self.ALL_INTEGER + self.ALL_FLOAT
|
|
self.arguments = {0: (np.arange(10),
|
|
self.ALL_INTEGER + self.ALL_FLOAT),
|
|
1: (np.arange(10),
|
|
self.ALL_INTEGER + self.ALL_FLOAT)}
|
|
input_array = [self.arguments[idx][0] for idx in self.arguments]
|
|
# In this case, self.partialfunc can simply be stats.somersd,
|
|
# since `alternative` is an optional argument. If it is required,
|
|
# we can use functools.partial to freeze the value, because
|
|
# we only mainly test various array inputs, not str, etc.
|
|
self.partialfunc = functools.partial(stats.somersd,
|
|
alternative='two-sided')
|
|
self.expected = self.partialfunc(*input_array)
|
|
|
|
def pythranfunc(self, *args):
|
|
res = self.partialfunc(*args)
|
|
assert_allclose(res.statistic, self.expected.statistic, atol=1e-15)
|
|
assert_allclose(res.pvalue, self.expected.pvalue, atol=1e-15)
|
|
|
|
def test_pythranfunc_keywords(self):
|
|
# Not specifying the optional keyword args
|
|
table = [[27, 25, 14, 7, 0], [7, 14, 18, 35, 12], [1, 3, 2, 7, 17]]
|
|
res1 = stats.somersd(table)
|
|
# Specifying the optional keyword args with default value
|
|
optional_args = self.get_optional_args(stats.somersd)
|
|
res2 = stats.somersd(table, **optional_args)
|
|
# Check if the results are the same in two cases
|
|
assert_allclose(res1.statistic, res2.statistic, atol=1e-15)
|
|
assert_allclose(res1.pvalue, res2.pvalue, atol=1e-15)
|
|
|
|
def test_like_kendalltau(self):
|
|
# All tests correspond with one in test_stats.py `test_kendalltau`
|
|
|
|
# case without ties, con-dis equal zero
|
|
x = [5, 2, 1, 3, 6, 4, 7, 8]
|
|
y = [5, 2, 6, 3, 1, 8, 7, 4]
|
|
# Cross-check with result from SAS FREQ:
|
|
expected = (0.000000000000000, 1.000000000000000)
|
|
res = stats.somersd(x, y)
|
|
assert_allclose(res.statistic, expected[0], atol=1e-15)
|
|
assert_allclose(res.pvalue, expected[1], atol=1e-15)
|
|
|
|
# case without ties, con-dis equal zero
|
|
x = [0, 5, 2, 1, 3, 6, 4, 7, 8]
|
|
y = [5, 2, 0, 6, 3, 1, 8, 7, 4]
|
|
# Cross-check with result from SAS FREQ:
|
|
expected = (0.000000000000000, 1.000000000000000)
|
|
res = stats.somersd(x, y)
|
|
assert_allclose(res.statistic, expected[0], atol=1e-15)
|
|
assert_allclose(res.pvalue, expected[1], atol=1e-15)
|
|
|
|
# case without ties, con-dis close to zero
|
|
x = [5, 2, 1, 3, 6, 4, 7]
|
|
y = [5, 2, 6, 3, 1, 7, 4]
|
|
# Cross-check with result from SAS FREQ:
|
|
expected = (-0.142857142857140, 0.630326953157670)
|
|
res = stats.somersd(x, y)
|
|
assert_allclose(res.statistic, expected[0], atol=1e-15)
|
|
assert_allclose(res.pvalue, expected[1], atol=1e-15)
|
|
|
|
# simple case without ties
|
|
x = np.arange(10)
|
|
y = np.arange(10)
|
|
# Cross-check with result from SAS FREQ:
|
|
# SAS p value is not provided.
|
|
expected = (1.000000000000000, 0)
|
|
res = stats.somersd(x, y)
|
|
assert_allclose(res.statistic, expected[0], atol=1e-15)
|
|
assert_allclose(res.pvalue, expected[1], atol=1e-15)
|
|
|
|
# swap a couple values and a couple more
|
|
x = np.arange(10)
|
|
y = np.array([0, 2, 1, 3, 4, 6, 5, 7, 8, 9])
|
|
# Cross-check with result from SAS FREQ:
|
|
expected = (0.911111111111110, 0.000000000000000)
|
|
res = stats.somersd(x, y)
|
|
assert_allclose(res.statistic, expected[0], atol=1e-15)
|
|
assert_allclose(res.pvalue, expected[1], atol=1e-15)
|
|
|
|
# same in opposite direction
|
|
x = np.arange(10)
|
|
y = np.arange(10)[::-1]
|
|
# Cross-check with result from SAS FREQ:
|
|
# SAS p value is not provided.
|
|
expected = (-1.000000000000000, 0)
|
|
res = stats.somersd(x, y)
|
|
assert_allclose(res.statistic, expected[0], atol=1e-15)
|
|
assert_allclose(res.pvalue, expected[1], atol=1e-15)
|
|
|
|
# swap a couple values and a couple more
|
|
x = np.arange(10)
|
|
y = np.array([9, 7, 8, 6, 5, 3, 4, 2, 1, 0])
|
|
# Cross-check with result from SAS FREQ:
|
|
expected = (-0.9111111111111111, 0.000000000000000)
|
|
res = stats.somersd(x, y)
|
|
assert_allclose(res.statistic, expected[0], atol=1e-15)
|
|
assert_allclose(res.pvalue, expected[1], atol=1e-15)
|
|
|
|
# with some ties
|
|
x1 = [12, 2, 1, 12, 2]
|
|
x2 = [1, 4, 7, 1, 0]
|
|
# Cross-check with result from SAS FREQ:
|
|
expected = (-0.500000000000000, 0.304901788178780)
|
|
res = stats.somersd(x1, x2)
|
|
assert_allclose(res.statistic, expected[0], atol=1e-15)
|
|
assert_allclose(res.pvalue, expected[1], atol=1e-15)
|
|
|
|
# with only ties in one or both inputs
|
|
# SAS will not produce an output for these:
|
|
# NOTE: No statistics are computed for x * y because x has fewer
|
|
# than 2 nonmissing levels.
|
|
# WARNING: No OUTPUT data set is produced for this table because a
|
|
# row or column variable has fewer than 2 nonmissing levels and no
|
|
# statistics are computed.
|
|
|
|
res = stats.somersd([2, 2, 2], [2, 2, 2])
|
|
assert_allclose(res.statistic, np.nan)
|
|
assert_allclose(res.pvalue, np.nan)
|
|
|
|
res = stats.somersd([2, 0, 2], [2, 2, 2])
|
|
assert_allclose(res.statistic, np.nan)
|
|
assert_allclose(res.pvalue, np.nan)
|
|
|
|
res = stats.somersd([2, 2, 2], [2, 0, 2])
|
|
assert_allclose(res.statistic, np.nan)
|
|
assert_allclose(res.pvalue, np.nan)
|
|
|
|
res = stats.somersd([0], [0])
|
|
assert_allclose(res.statistic, np.nan)
|
|
assert_allclose(res.pvalue, np.nan)
|
|
|
|
# empty arrays provided as input
|
|
res = stats.somersd([], [])
|
|
assert_allclose(res.statistic, np.nan)
|
|
assert_allclose(res.pvalue, np.nan)
|
|
|
|
# test unequal length inputs
|
|
x = np.arange(10.)
|
|
y = np.arange(20.)
|
|
assert_raises(ValueError, stats.somersd, x, y)
|
|
|
|
def test_asymmetry(self):
|
|
# test that somersd is asymmetric w.r.t. input order and that
|
|
# convention is as described: first input is row variable & independent
|
|
# data is from Wikipedia:
|
|
# https://en.wikipedia.org/wiki/Somers%27_D
|
|
# but currently that example contradicts itself - it says X is
|
|
# independent yet take D_XY
|
|
|
|
x = [1, 1, 1, 2, 2, 2, 2, 2, 3, 3, 1, 2,
|
|
2, 2, 2, 2, 2, 2, 3, 3, 3, 3, 3, 3]
|
|
y = [1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 2, 2,
|
|
2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2]
|
|
# Cross-check with result from SAS FREQ:
|
|
d_cr = 0.272727272727270
|
|
d_rc = 0.342857142857140
|
|
p = 0.092891940883700 # same p-value for either direction
|
|
res = stats.somersd(x, y)
|
|
assert_allclose(res.statistic, d_cr, atol=1e-15)
|
|
assert_allclose(res.pvalue, p, atol=1e-4)
|
|
assert_equal(res.table.shape, (3, 2))
|
|
res = stats.somersd(y, x)
|
|
assert_allclose(res.statistic, d_rc, atol=1e-15)
|
|
assert_allclose(res.pvalue, p, atol=1e-15)
|
|
assert_equal(res.table.shape, (2, 3))
|
|
|
|
def test_somers_original(self):
|
|
# test against Somers' original paper [1]
|
|
|
|
# Table 5A
|
|
# Somers' convention was column IV
|
|
table = np.array([[8, 2], [6, 5], [3, 4], [1, 3], [2, 3]])
|
|
# Our convention (and that of SAS FREQ) is row IV
|
|
table = table.T
|
|
dyx = 129/340
|
|
assert_allclose(stats.somersd(table).statistic, dyx)
|
|
|
|
# table 7A - d_yx = 1
|
|
table = np.array([[25, 0], [85, 0], [0, 30]])
|
|
dxy, dyx = 3300/5425, 3300/3300
|
|
assert_allclose(stats.somersd(table).statistic, dxy)
|
|
assert_allclose(stats.somersd(table.T).statistic, dyx)
|
|
|
|
# table 7B - d_yx < 0
|
|
table = np.array([[25, 0], [0, 30], [85, 0]])
|
|
dyx = -1800/3300
|
|
assert_allclose(stats.somersd(table.T).statistic, dyx)
|
|
|
|
def test_contingency_table_with_zero_rows_cols(self):
|
|
# test that zero rows/cols in contingency table don't affect result
|
|
|
|
N = 100
|
|
shape = 4, 6
|
|
size = np.prod(shape)
|
|
|
|
np.random.seed(0)
|
|
s = stats.multinomial.rvs(N, p=np.ones(size)/size).reshape(shape)
|
|
res = stats.somersd(s)
|
|
|
|
s2 = np.insert(s, 2, np.zeros(shape[1]), axis=0)
|
|
res2 = stats.somersd(s2)
|
|
|
|
s3 = np.insert(s, 2, np.zeros(shape[0]), axis=1)
|
|
res3 = stats.somersd(s3)
|
|
|
|
s4 = np.insert(s2, 2, np.zeros(shape[0]+1), axis=1)
|
|
res4 = stats.somersd(s4)
|
|
|
|
# Cross-check with result from SAS FREQ:
|
|
assert_allclose(res.statistic, -0.116981132075470, atol=1e-15)
|
|
assert_allclose(res.statistic, res2.statistic)
|
|
assert_allclose(res.statistic, res3.statistic)
|
|
assert_allclose(res.statistic, res4.statistic)
|
|
|
|
assert_allclose(res.pvalue, 0.156376448188150, atol=1e-15)
|
|
assert_allclose(res.pvalue, res2.pvalue)
|
|
assert_allclose(res.pvalue, res3.pvalue)
|
|
assert_allclose(res.pvalue, res4.pvalue)
|
|
|
|
def test_invalid_contingency_tables(self):
|
|
N = 100
|
|
shape = 4, 6
|
|
size = np.prod(shape)
|
|
|
|
np.random.seed(0)
|
|
# start with a valid contingency table
|
|
s = stats.multinomial.rvs(N, p=np.ones(size)/size).reshape(shape)
|
|
|
|
s5 = s - 2
|
|
message = "All elements of the contingency table must be non-negative"
|
|
with assert_raises(ValueError, match=message):
|
|
stats.somersd(s5)
|
|
|
|
s6 = s + 0.01
|
|
message = "All elements of the contingency table must be integer"
|
|
with assert_raises(ValueError, match=message):
|
|
stats.somersd(s6)
|
|
|
|
message = ("At least two elements of the contingency "
|
|
"table must be nonzero.")
|
|
with assert_raises(ValueError, match=message):
|
|
stats.somersd([[]])
|
|
|
|
with assert_raises(ValueError, match=message):
|
|
stats.somersd([[1]])
|
|
|
|
s7 = np.zeros((3, 3))
|
|
with assert_raises(ValueError, match=message):
|
|
stats.somersd(s7)
|
|
|
|
s7[0, 1] = 1
|
|
with assert_raises(ValueError, match=message):
|
|
stats.somersd(s7)
|
|
|
|
def test_only_ranks_matter(self):
|
|
# only ranks of input data should matter
|
|
x = [1, 2, 3]
|
|
x2 = [-1, 2.1, np.inf]
|
|
y = [3, 2, 1]
|
|
y2 = [0, -0.5, -np.inf]
|
|
res = stats.somersd(x, y)
|
|
res2 = stats.somersd(x2, y2)
|
|
assert_equal(res.statistic, res2.statistic)
|
|
assert_equal(res.pvalue, res2.pvalue)
|
|
|
|
def test_contingency_table_return(self):
|
|
# check that contingency table is returned
|
|
x = np.arange(10)
|
|
y = np.arange(10)
|
|
res = stats.somersd(x, y)
|
|
assert_equal(res.table, np.eye(10))
|
|
|
|
def test_somersd_alternative(self):
|
|
# Test alternative parameter, asymptotic method (due to tie)
|
|
|
|
# Based on scipy.stats.test_stats.TestCorrSpearman2::test_alternative
|
|
x1 = [1, 2, 3, 4, 5]
|
|
x2 = [5, 6, 7, 8, 7]
|
|
|
|
# strong positive correlation
|
|
expected = stats.somersd(x1, x2, alternative="two-sided")
|
|
assert expected.statistic > 0
|
|
|
|
# rank correlation > 0 -> large "less" p-value
|
|
res = stats.somersd(x1, x2, alternative="less")
|
|
assert_equal(res.statistic, expected.statistic)
|
|
assert_allclose(res.pvalue, 1 - (expected.pvalue / 2))
|
|
|
|
# rank correlation > 0 -> small "greater" p-value
|
|
res = stats.somersd(x1, x2, alternative="greater")
|
|
assert_equal(res.statistic, expected.statistic)
|
|
assert_allclose(res.pvalue, expected.pvalue / 2)
|
|
|
|
# reverse the direction of rank correlation
|
|
x2.reverse()
|
|
|
|
# strong negative correlation
|
|
expected = stats.somersd(x1, x2, alternative="two-sided")
|
|
assert expected.statistic < 0
|
|
|
|
# rank correlation < 0 -> large "greater" p-value
|
|
res = stats.somersd(x1, x2, alternative="greater")
|
|
assert_equal(res.statistic, expected.statistic)
|
|
assert_allclose(res.pvalue, 1 - (expected.pvalue / 2))
|
|
|
|
# rank correlation < 0 -> small "less" p-value
|
|
res = stats.somersd(x1, x2, alternative="less")
|
|
assert_equal(res.statistic, expected.statistic)
|
|
assert_allclose(res.pvalue, expected.pvalue / 2)
|
|
|
|
with pytest.raises(ValueError, match="`alternative` must be..."):
|
|
stats.somersd(x1, x2, alternative="ekki-ekki")
|
|
|
|
@pytest.mark.parametrize("positive_correlation", (False, True))
|
|
def test_somersd_perfect_correlation(self, positive_correlation):
|
|
# Before the addition of `alternative`, perfect correlation was
|
|
# treated as a special case. Now it is treated like any other case, but
|
|
# make sure there are no divide by zero warnings or associated errors
|
|
|
|
x1 = np.arange(10)
|
|
x2 = x1 if positive_correlation else np.flip(x1)
|
|
expected_statistic = 1 if positive_correlation else -1
|
|
|
|
# perfect correlation -> small "two-sided" p-value (0)
|
|
res = stats.somersd(x1, x2, alternative="two-sided")
|
|
assert res.statistic == expected_statistic
|
|
assert res.pvalue == 0
|
|
|
|
# rank correlation > 0 -> large "less" p-value (1)
|
|
res = stats.somersd(x1, x2, alternative="less")
|
|
assert res.statistic == expected_statistic
|
|
assert res.pvalue == (1 if positive_correlation else 0)
|
|
|
|
# rank correlation > 0 -> small "greater" p-value (0)
|
|
res = stats.somersd(x1, x2, alternative="greater")
|
|
assert res.statistic == expected_statistic
|
|
assert res.pvalue == (0 if positive_correlation else 1)
|
|
|
|
def test_somersd_large_inputs_gh18132(self):
|
|
# Test that large inputs where potential overflows could occur give
|
|
# the expected output. This is tested in the case of binary inputs.
|
|
# See gh-18126.
|
|
|
|
# generate lists of random classes 1-2 (binary)
|
|
classes = [1, 2]
|
|
n_samples = 10 ** 6
|
|
random.seed(6272161)
|
|
x = random.choices(classes, k=n_samples)
|
|
y = random.choices(classes, k=n_samples)
|
|
|
|
# get value to compare with: sklearn output
|
|
# from sklearn import metrics
|
|
# val_auc_sklearn = metrics.roc_auc_score(x, y)
|
|
# # convert to the Gini coefficient (Gini = (AUC*2)-1)
|
|
# val_sklearn = 2 * val_auc_sklearn - 1
|
|
val_sklearn = -0.001528138777036947
|
|
|
|
# calculate the Somers' D statistic, which should be equal to the
|
|
# result of val_sklearn until approximately machine precision
|
|
val_scipy = stats.somersd(x, y).statistic
|
|
assert_allclose(val_sklearn, val_scipy, atol=1e-15)
|
|
|
|
|
|
class TestBarnardExact:
|
|
"""Some tests to show that barnard_exact() works correctly."""
|
|
|
|
@pytest.mark.parametrize(
|
|
"input_sample,expected",
|
|
[
|
|
([[43, 40], [10, 39]], (3.555406779643, 0.000362832367)),
|
|
([[100, 2], [1000, 5]], (-1.776382925679, 0.135126970878)),
|
|
([[2, 7], [8, 2]], (-2.518474945157, 0.019210815430)),
|
|
([[5, 1], [10, 10]], (1.449486150679, 0.156277546306)),
|
|
([[5, 15], [20, 20]], (-1.851640199545, 0.066363501421)),
|
|
([[5, 16], [20, 25]], (-1.609639949352, 0.116984852192)),
|
|
([[10, 5], [10, 1]], (-1.449486150679, 0.177536588915)),
|
|
([[5, 0], [1, 4]], (2.581988897472, 0.013671875000)),
|
|
([[0, 1], [3, 2]], (-1.095445115010, 0.509667991877)),
|
|
([[0, 2], [6, 4]], (-1.549193338483, 0.197019618792)),
|
|
([[2, 7], [8, 2]], (-2.518474945157, 0.019210815430)),
|
|
],
|
|
)
|
|
def test_precise(self, input_sample, expected):
|
|
"""The expected values have been generated by R, using a resolution
|
|
for the nuisance parameter of 1e-6 :
|
|
```R
|
|
library(Barnard)
|
|
options(digits=10)
|
|
barnard.test(43, 40, 10, 39, dp=1e-6, pooled=TRUE)
|
|
```
|
|
"""
|
|
res = barnard_exact(input_sample)
|
|
statistic, pvalue = res.statistic, res.pvalue
|
|
assert_allclose([statistic, pvalue], expected)
|
|
|
|
@pytest.mark.parametrize(
|
|
"input_sample,expected",
|
|
[
|
|
([[43, 40], [10, 39]], (3.920362887717, 0.000289470662)),
|
|
([[100, 2], [1000, 5]], (-1.139432816087, 0.950272080594)),
|
|
([[2, 7], [8, 2]], (-3.079373904042, 0.020172119141)),
|
|
([[5, 1], [10, 10]], (1.622375939458, 0.150599922226)),
|
|
([[5, 15], [20, 20]], (-1.974771239528, 0.063038448651)),
|
|
([[5, 16], [20, 25]], (-1.722122973346, 0.133329494287)),
|
|
([[10, 5], [10, 1]], (-1.765469659009, 0.250566655215)),
|
|
([[5, 0], [1, 4]], (5.477225575052, 0.007812500000)),
|
|
([[0, 1], [3, 2]], (-1.224744871392, 0.509667991877)),
|
|
([[0, 2], [6, 4]], (-1.732050807569, 0.197019618792)),
|
|
([[2, 7], [8, 2]], (-3.079373904042, 0.020172119141)),
|
|
],
|
|
)
|
|
def test_pooled_param(self, input_sample, expected):
|
|
"""The expected values have been generated by R, using a resolution
|
|
for the nuisance parameter of 1e-6 :
|
|
```R
|
|
library(Barnard)
|
|
options(digits=10)
|
|
barnard.test(43, 40, 10, 39, dp=1e-6, pooled=FALSE)
|
|
```
|
|
"""
|
|
res = barnard_exact(input_sample, pooled=False)
|
|
statistic, pvalue = res.statistic, res.pvalue
|
|
assert_allclose([statistic, pvalue], expected)
|
|
|
|
def test_raises(self):
|
|
# test we raise an error for wrong input number of nuisances.
|
|
error_msg = (
|
|
"Number of points `n` must be strictly positive, found 0"
|
|
)
|
|
with assert_raises(ValueError, match=error_msg):
|
|
barnard_exact([[1, 2], [3, 4]], n=0)
|
|
|
|
# test we raise an error for wrong shape of input.
|
|
error_msg = "The input `table` must be of shape \\(2, 2\\)."
|
|
with assert_raises(ValueError, match=error_msg):
|
|
barnard_exact(np.arange(6).reshape(2, 3))
|
|
|
|
# Test all values must be positives
|
|
error_msg = "All values in `table` must be nonnegative."
|
|
with assert_raises(ValueError, match=error_msg):
|
|
barnard_exact([[-1, 2], [3, 4]])
|
|
|
|
# Test value error on wrong alternative param
|
|
error_msg = (
|
|
"`alternative` should be one of {'two-sided', 'less', 'greater'},"
|
|
" found .*"
|
|
)
|
|
with assert_raises(ValueError, match=error_msg):
|
|
barnard_exact([[1, 2], [3, 4]], "not-correct")
|
|
|
|
@pytest.mark.parametrize(
|
|
"input_sample,expected",
|
|
[
|
|
([[0, 0], [4, 3]], (1.0, 0)),
|
|
],
|
|
)
|
|
def test_edge_cases(self, input_sample, expected):
|
|
res = barnard_exact(input_sample)
|
|
statistic, pvalue = res.statistic, res.pvalue
|
|
assert_equal(pvalue, expected[0])
|
|
assert_equal(statistic, expected[1])
|
|
|
|
@pytest.mark.parametrize(
|
|
"input_sample,expected",
|
|
[
|
|
([[0, 5], [0, 10]], (1.0, np.nan)),
|
|
([[5, 0], [10, 0]], (1.0, np.nan)),
|
|
],
|
|
)
|
|
def test_row_or_col_zero(self, input_sample, expected):
|
|
res = barnard_exact(input_sample)
|
|
statistic, pvalue = res.statistic, res.pvalue
|
|
assert_equal(pvalue, expected[0])
|
|
assert_equal(statistic, expected[1])
|
|
|
|
@pytest.mark.parametrize(
|
|
"input_sample,expected",
|
|
[
|
|
([[2, 7], [8, 2]], (-2.518474945157, 0.009886140845)),
|
|
([[7, 200], [300, 8]], (-21.320036698460, 0.0)),
|
|
([[21, 28], [1957, 6]], (-30.489638143953, 0.0)),
|
|
],
|
|
)
|
|
@pytest.mark.parametrize("alternative", ["greater", "less"])
|
|
def test_less_greater(self, input_sample, expected, alternative):
|
|
"""
|
|
"The expected values have been generated by R, using a resolution
|
|
for the nuisance parameter of 1e-6 :
|
|
```R
|
|
library(Barnard)
|
|
options(digits=10)
|
|
a = barnard.test(2, 7, 8, 2, dp=1e-6, pooled=TRUE)
|
|
a$p.value[1]
|
|
```
|
|
In this test, we are using the "one-sided" return value `a$p.value[1]`
|
|
to test our pvalue.
|
|
"""
|
|
expected_stat, less_pvalue_expect = expected
|
|
|
|
if alternative == "greater":
|
|
input_sample = np.array(input_sample)[:, ::-1]
|
|
expected_stat = -expected_stat
|
|
|
|
res = barnard_exact(input_sample, alternative=alternative)
|
|
statistic, pvalue = res.statistic, res.pvalue
|
|
assert_allclose(
|
|
[statistic, pvalue], [expected_stat, less_pvalue_expect], atol=1e-7
|
|
)
|
|
|
|
|
|
class TestBoschlooExact:
|
|
"""Some tests to show that boschloo_exact() works correctly."""
|
|
|
|
ATOL = 1e-7
|
|
|
|
@pytest.mark.parametrize(
|
|
"input_sample,expected",
|
|
[
|
|
([[2, 7], [8, 2]], (0.01852173, 0.009886142)),
|
|
([[5, 1], [10, 10]], (0.9782609, 0.9450994)),
|
|
([[5, 16], [20, 25]], (0.08913823, 0.05827348)),
|
|
([[10, 5], [10, 1]], (0.1652174, 0.08565611)),
|
|
([[5, 0], [1, 4]], (1, 1)),
|
|
([[0, 1], [3, 2]], (0.5, 0.34375)),
|
|
([[2, 7], [8, 2]], (0.01852173, 0.009886142)),
|
|
([[7, 12], [8, 3]], (0.06406797, 0.03410916)),
|
|
([[10, 24], [25, 37]], (0.2009359, 0.1512882)),
|
|
],
|
|
)
|
|
def test_less(self, input_sample, expected):
|
|
"""The expected values have been generated by R, using a resolution
|
|
for the nuisance parameter of 1e-8 :
|
|
```R
|
|
library(Exact)
|
|
options(digits=10)
|
|
data <- matrix(c(43, 10, 40, 39), 2, 2, byrow=TRUE)
|
|
a = exact.test(data, method="Boschloo", alternative="less",
|
|
tsmethod="central", np.interval=TRUE, beta=1e-8)
|
|
```
|
|
"""
|
|
res = boschloo_exact(input_sample, alternative="less")
|
|
statistic, pvalue = res.statistic, res.pvalue
|
|
assert_allclose([statistic, pvalue], expected, atol=self.ATOL)
|
|
|
|
@pytest.mark.parametrize(
|
|
"input_sample,expected",
|
|
[
|
|
([[43, 40], [10, 39]], (0.0002875544, 0.0001615562)),
|
|
([[2, 7], [8, 2]], (0.9990149, 0.9918327)),
|
|
([[5, 1], [10, 10]], (0.1652174, 0.09008534)),
|
|
([[5, 15], [20, 20]], (0.9849087, 0.9706997)),
|
|
([[5, 16], [20, 25]], (0.972349, 0.9524124)),
|
|
([[5, 0], [1, 4]], (0.02380952, 0.006865367)),
|
|
([[0, 1], [3, 2]], (1, 1)),
|
|
([[0, 2], [6, 4]], (1, 1)),
|
|
([[2, 7], [8, 2]], (0.9990149, 0.9918327)),
|
|
([[7, 12], [8, 3]], (0.9895302, 0.9771215)),
|
|
([[10, 24], [25, 37]], (0.9012936, 0.8633275)),
|
|
],
|
|
)
|
|
def test_greater(self, input_sample, expected):
|
|
"""The expected values have been generated by R, using a resolution
|
|
for the nuisance parameter of 1e-8 :
|
|
```R
|
|
library(Exact)
|
|
options(digits=10)
|
|
data <- matrix(c(43, 10, 40, 39), 2, 2, byrow=TRUE)
|
|
a = exact.test(data, method="Boschloo", alternative="greater",
|
|
tsmethod="central", np.interval=TRUE, beta=1e-8)
|
|
```
|
|
"""
|
|
res = boschloo_exact(input_sample, alternative="greater")
|
|
statistic, pvalue = res.statistic, res.pvalue
|
|
assert_allclose([statistic, pvalue], expected, atol=self.ATOL)
|
|
|
|
@pytest.mark.parametrize(
|
|
"input_sample,expected",
|
|
[
|
|
([[43, 40], [10, 39]], (0.0002875544, 0.0003231115)),
|
|
([[2, 7], [8, 2]], (0.01852173, 0.01977228)),
|
|
([[5, 1], [10, 10]], (0.1652174, 0.1801707)),
|
|
([[5, 16], [20, 25]], (0.08913823, 0.116547)),
|
|
([[5, 0], [1, 4]], (0.02380952, 0.01373073)),
|
|
([[0, 1], [3, 2]], (0.5, 0.6875)),
|
|
([[2, 7], [8, 2]], (0.01852173, 0.01977228)),
|
|
([[7, 12], [8, 3]], (0.06406797, 0.06821831)),
|
|
],
|
|
)
|
|
def test_two_sided(self, input_sample, expected):
|
|
"""The expected values have been generated by R, using a resolution
|
|
for the nuisance parameter of 1e-8 :
|
|
```R
|
|
library(Exact)
|
|
options(digits=10)
|
|
data <- matrix(c(43, 10, 40, 39), 2, 2, byrow=TRUE)
|
|
a = exact.test(data, method="Boschloo", alternative="two.sided",
|
|
tsmethod="central", np.interval=TRUE, beta=1e-8)
|
|
```
|
|
"""
|
|
res = boschloo_exact(input_sample, alternative="two-sided", n=64)
|
|
# Need n = 64 for python 32-bit
|
|
statistic, pvalue = res.statistic, res.pvalue
|
|
assert_allclose([statistic, pvalue], expected, atol=self.ATOL)
|
|
|
|
def test_raises(self):
|
|
# test we raise an error for wrong input number of nuisances.
|
|
error_msg = (
|
|
"Number of points `n` must be strictly positive, found 0"
|
|
)
|
|
with assert_raises(ValueError, match=error_msg):
|
|
boschloo_exact([[1, 2], [3, 4]], n=0)
|
|
|
|
# test we raise an error for wrong shape of input.
|
|
error_msg = "The input `table` must be of shape \\(2, 2\\)."
|
|
with assert_raises(ValueError, match=error_msg):
|
|
boschloo_exact(np.arange(6).reshape(2, 3))
|
|
|
|
# Test all values must be positives
|
|
error_msg = "All values in `table` must be nonnegative."
|
|
with assert_raises(ValueError, match=error_msg):
|
|
boschloo_exact([[-1, 2], [3, 4]])
|
|
|
|
# Test value error on wrong alternative param
|
|
error_msg = (
|
|
r"`alternative` should be one of \('two-sided', 'less', "
|
|
r"'greater'\), found .*"
|
|
)
|
|
with assert_raises(ValueError, match=error_msg):
|
|
boschloo_exact([[1, 2], [3, 4]], "not-correct")
|
|
|
|
@pytest.mark.parametrize(
|
|
"input_sample,expected",
|
|
[
|
|
([[0, 5], [0, 10]], (np.nan, np.nan)),
|
|
([[5, 0], [10, 0]], (np.nan, np.nan)),
|
|
],
|
|
)
|
|
def test_row_or_col_zero(self, input_sample, expected):
|
|
res = boschloo_exact(input_sample)
|
|
statistic, pvalue = res.statistic, res.pvalue
|
|
assert_equal(pvalue, expected[0])
|
|
assert_equal(statistic, expected[1])
|
|
|
|
def test_two_sided_gt_1(self):
|
|
# Check that returned p-value does not exceed 1 even when twice
|
|
# the minimum of the one-sided p-values does. See gh-15345.
|
|
tbl = [[1, 1], [13, 12]]
|
|
pl = boschloo_exact(tbl, alternative='less').pvalue
|
|
pg = boschloo_exact(tbl, alternative='greater').pvalue
|
|
assert 2*min(pl, pg) > 1
|
|
pt = boschloo_exact(tbl, alternative='two-sided').pvalue
|
|
assert pt == 1.0
|
|
|
|
@pytest.mark.parametrize("alternative", ("less", "greater"))
|
|
def test_against_fisher_exact(self, alternative):
|
|
# Check that the statistic of `boschloo_exact` is the same as the
|
|
# p-value of `fisher_exact` (for one-sided tests). See gh-15345.
|
|
tbl = [[2, 7], [8, 2]]
|
|
boschloo_stat = boschloo_exact(tbl, alternative=alternative).statistic
|
|
fisher_p = stats.fisher_exact(tbl, alternative=alternative)[1]
|
|
assert_allclose(boschloo_stat, fisher_p)
|
|
|
|
|
|
class TestCvm_2samp:
|
|
@pytest.mark.parametrize('args', [([], np.arange(5)),
|
|
(np.arange(5), [1])])
|
|
def test_too_small_input(self, args):
|
|
with pytest.warns(SmallSampleWarning, match=too_small_1d_not_omit):
|
|
res = cramervonmises_2samp(*args)
|
|
assert_equal(res.statistic, np.nan)
|
|
assert_equal(res.pvalue, np.nan)
|
|
|
|
def test_invalid_input(self):
|
|
y = np.arange(5)
|
|
msg = 'method must be either auto, exact or asymptotic'
|
|
with pytest.raises(ValueError, match=msg):
|
|
cramervonmises_2samp(y, y, 'xyz')
|
|
|
|
def test_list_input(self):
|
|
x = [2, 3, 4, 7, 6]
|
|
y = [0.2, 0.7, 12, 18]
|
|
r1 = cramervonmises_2samp(x, y)
|
|
r2 = cramervonmises_2samp(np.array(x), np.array(y))
|
|
assert_equal((r1.statistic, r1.pvalue), (r2.statistic, r2.pvalue))
|
|
|
|
def test_example_conover(self):
|
|
# Example 2 in Section 6.2 of W.J. Conover: Practical Nonparametric
|
|
# Statistics, 1971.
|
|
x = [7.6, 8.4, 8.6, 8.7, 9.3, 9.9, 10.1, 10.6, 11.2]
|
|
y = [5.2, 5.7, 5.9, 6.5, 6.8, 8.2, 9.1, 9.8, 10.8, 11.3, 11.5, 12.3,
|
|
12.5, 13.4, 14.6]
|
|
r = cramervonmises_2samp(x, y)
|
|
assert_allclose(r.statistic, 0.262, atol=1e-3)
|
|
assert_allclose(r.pvalue, 0.18, atol=1e-2)
|
|
|
|
@pytest.mark.parametrize('statistic, m, n, pval',
|
|
[(710, 5, 6, 48./462),
|
|
(1897, 7, 7, 117./1716),
|
|
(576, 4, 6, 2./210),
|
|
(1764, 6, 7, 2./1716)])
|
|
def test_exact_pvalue(self, statistic, m, n, pval):
|
|
# the exact values are taken from Anderson: On the distribution of the
|
|
# two-sample Cramer-von-Mises criterion, 1962.
|
|
# The values are taken from Table 2, 3, 4 and 5
|
|
assert_equal(_pval_cvm_2samp_exact(statistic, m, n), pval)
|
|
|
|
@pytest.mark.xslow
|
|
def test_large_sample(self):
|
|
# for large samples, the statistic U gets very large
|
|
# do a sanity check that p-value is not 0, 1 or nan
|
|
np.random.seed(4367)
|
|
x = distributions.norm.rvs(size=1000000)
|
|
y = distributions.norm.rvs(size=900000)
|
|
r = cramervonmises_2samp(x, y)
|
|
assert_(0 < r.pvalue < 1)
|
|
r = cramervonmises_2samp(x, y+0.1)
|
|
assert_(0 < r.pvalue < 1)
|
|
|
|
def test_exact_vs_asymptotic(self):
|
|
np.random.seed(0)
|
|
x = np.random.rand(7)
|
|
y = np.random.rand(8)
|
|
r1 = cramervonmises_2samp(x, y, method='exact')
|
|
r2 = cramervonmises_2samp(x, y, method='asymptotic')
|
|
assert_equal(r1.statistic, r2.statistic)
|
|
assert_allclose(r1.pvalue, r2.pvalue, atol=1e-2)
|
|
|
|
def test_method_auto(self):
|
|
x = np.arange(20)
|
|
y = [0.5, 4.7, 13.1]
|
|
r1 = cramervonmises_2samp(x, y, method='exact')
|
|
r2 = cramervonmises_2samp(x, y, method='auto')
|
|
assert_equal(r1.pvalue, r2.pvalue)
|
|
# switch to asymptotic if one sample has more than 20 observations
|
|
x = np.arange(21)
|
|
r1 = cramervonmises_2samp(x, y, method='asymptotic')
|
|
r2 = cramervonmises_2samp(x, y, method='auto')
|
|
assert_equal(r1.pvalue, r2.pvalue)
|
|
|
|
def test_same_input(self):
|
|
# make sure trivial edge case can be handled
|
|
# note that _cdf_cvm_inf(0) = nan. implementation avoids nan by
|
|
# returning pvalue=1 for very small values of the statistic
|
|
x = np.arange(15)
|
|
res = cramervonmises_2samp(x, x)
|
|
assert_equal((res.statistic, res.pvalue), (0.0, 1.0))
|
|
# check exact p-value
|
|
res = cramervonmises_2samp(x[:4], x[:4])
|
|
assert_equal((res.statistic, res.pvalue), (0.0, 1.0))
|
|
|
|
|
|
class TestTukeyHSD:
|
|
|
|
data_same_size = ([24.5, 23.5, 26.4, 27.1, 29.9],
|
|
[28.4, 34.2, 29.5, 32.2, 30.1],
|
|
[26.1, 28.3, 24.3, 26.2, 27.8])
|
|
data_diff_size = ([24.5, 23.5, 26.28, 26.4, 27.1, 29.9, 30.1, 30.1],
|
|
[28.4, 34.2, 29.5, 32.2, 30.1],
|
|
[26.1, 28.3, 24.3, 26.2, 27.8])
|
|
extreme_size = ([24.5, 23.5, 26.4],
|
|
[28.4, 34.2, 29.5, 32.2, 30.1, 28.4, 34.2, 29.5, 32.2,
|
|
30.1],
|
|
[26.1, 28.3, 24.3, 26.2, 27.8])
|
|
|
|
sas_same_size = """
|
|
Comparison LowerCL Difference UpperCL Significance
|
|
2 - 3 0.6908830568 4.34 7.989116943 1
|
|
2 - 1 0.9508830568 4.6 8.249116943 1
|
|
3 - 2 -7.989116943 -4.34 -0.6908830568 1
|
|
3 - 1 -3.389116943 0.26 3.909116943 0
|
|
1 - 2 -8.249116943 -4.6 -0.9508830568 1
|
|
1 - 3 -3.909116943 -0.26 3.389116943 0
|
|
"""
|
|
|
|
sas_diff_size = """
|
|
Comparison LowerCL Difference UpperCL Significance
|
|
2 - 1 0.2679292645 3.645 7.022070736 1
|
|
2 - 3 0.5934764007 4.34 8.086523599 1
|
|
1 - 2 -7.022070736 -3.645 -0.2679292645 1
|
|
1 - 3 -2.682070736 0.695 4.072070736 0
|
|
3 - 2 -8.086523599 -4.34 -0.5934764007 1
|
|
3 - 1 -4.072070736 -0.695 2.682070736 0
|
|
"""
|
|
|
|
sas_extreme = """
|
|
Comparison LowerCL Difference UpperCL Significance
|
|
2 - 3 1.561605075 4.34 7.118394925 1
|
|
2 - 1 2.740784879 6.08 9.419215121 1
|
|
3 - 2 -7.118394925 -4.34 -1.561605075 1
|
|
3 - 1 -1.964526566 1.74 5.444526566 0
|
|
1 - 2 -9.419215121 -6.08 -2.740784879 1
|
|
1 - 3 -5.444526566 -1.74 1.964526566 0
|
|
"""
|
|
|
|
@pytest.mark.parametrize("data,res_expect_str,atol",
|
|
((data_same_size, sas_same_size, 1e-4),
|
|
(data_diff_size, sas_diff_size, 1e-4),
|
|
(extreme_size, sas_extreme, 1e-10),
|
|
),
|
|
ids=["equal size sample",
|
|
"unequal sample size",
|
|
"extreme sample size differences"])
|
|
def test_compare_sas(self, data, res_expect_str, atol):
|
|
'''
|
|
SAS code used to generate results for each sample:
|
|
DATA ACHE;
|
|
INPUT BRAND RELIEF;
|
|
CARDS;
|
|
1 24.5
|
|
...
|
|
3 27.8
|
|
;
|
|
ods graphics on; ODS RTF;ODS LISTING CLOSE;
|
|
PROC ANOVA DATA=ACHE;
|
|
CLASS BRAND;
|
|
MODEL RELIEF=BRAND;
|
|
MEANS BRAND/TUKEY CLDIFF;
|
|
TITLE 'COMPARE RELIEF ACROSS MEDICINES - ANOVA EXAMPLE';
|
|
ods output CLDiffs =tc;
|
|
proc print data=tc;
|
|
format LowerCL 17.16 UpperCL 17.16 Difference 17.16;
|
|
title "Output with many digits";
|
|
RUN;
|
|
QUIT;
|
|
ODS RTF close;
|
|
ODS LISTING;
|
|
'''
|
|
res_expect = np.asarray(res_expect_str.replace(" - ", " ").split()[5:],
|
|
dtype=float).reshape((6, 6))
|
|
res_tukey = stats.tukey_hsd(*data)
|
|
conf = res_tukey.confidence_interval()
|
|
# loop over the comparisons
|
|
for i, j, l, s, h, sig in res_expect:
|
|
i, j = int(i) - 1, int(j) - 1
|
|
assert_allclose(conf.low[i, j], l, atol=atol)
|
|
assert_allclose(res_tukey.statistic[i, j], s, atol=atol)
|
|
assert_allclose(conf.high[i, j], h, atol=atol)
|
|
assert_allclose((res_tukey.pvalue[i, j] <= .05), sig == 1)
|
|
|
|
matlab_sm_siz = """
|
|
1 2 -8.2491590248597 -4.6 -0.9508409751403 0.0144483269098
|
|
1 3 -3.9091590248597 -0.26 3.3891590248597 0.9803107240900
|
|
2 3 0.6908409751403 4.34 7.9891590248597 0.0203311368795
|
|
"""
|
|
|
|
matlab_diff_sz = """
|
|
1 2 -7.02207069748501 -3.645 -0.26792930251500 0.03371498443080
|
|
1 3 -2.68207069748500 0.695 4.07207069748500 0.85572267328807
|
|
2 3 0.59347644287720 4.34 8.08652355712281 0.02259047020620
|
|
"""
|
|
|
|
@pytest.mark.parametrize("data,res_expect_str,atol",
|
|
((data_same_size, matlab_sm_siz, 1e-12),
|
|
(data_diff_size, matlab_diff_sz, 1e-7)),
|
|
ids=["equal size sample",
|
|
"unequal size sample"])
|
|
def test_compare_matlab(self, data, res_expect_str, atol):
|
|
"""
|
|
vals = [24.5, 23.5, 26.4, 27.1, 29.9, 28.4, 34.2, 29.5, 32.2, 30.1,
|
|
26.1, 28.3, 24.3, 26.2, 27.8]
|
|
names = {'zero', 'zero', 'zero', 'zero', 'zero', 'one', 'one', 'one',
|
|
'one', 'one', 'two', 'two', 'two', 'two', 'two'}
|
|
[p,t,stats] = anova1(vals,names,"off");
|
|
[c,m,h,nms] = multcompare(stats, "CType","hsd");
|
|
"""
|
|
res_expect = np.asarray(res_expect_str.split(),
|
|
dtype=float).reshape((3, 6))
|
|
res_tukey = stats.tukey_hsd(*data)
|
|
conf = res_tukey.confidence_interval()
|
|
# loop over the comparisons
|
|
for i, j, l, s, h, p in res_expect:
|
|
i, j = int(i) - 1, int(j) - 1
|
|
assert_allclose(conf.low[i, j], l, atol=atol)
|
|
assert_allclose(res_tukey.statistic[i, j], s, atol=atol)
|
|
assert_allclose(conf.high[i, j], h, atol=atol)
|
|
assert_allclose(res_tukey.pvalue[i, j], p, atol=atol)
|
|
|
|
def test_compare_r(self):
|
|
"""
|
|
Testing against results and p-values from R:
|
|
from: https://www.rdocumentation.org/packages/stats/versions/3.6.2/
|
|
topics/TukeyHSD
|
|
> require(graphics)
|
|
> summary(fm1 <- aov(breaks ~ tension, data = warpbreaks))
|
|
> TukeyHSD(fm1, "tension", ordered = TRUE)
|
|
> plot(TukeyHSD(fm1, "tension"))
|
|
Tukey multiple comparisons of means
|
|
95% family-wise confidence level
|
|
factor levels have been ordered
|
|
Fit: aov(formula = breaks ~ tension, data = warpbreaks)
|
|
$tension
|
|
"""
|
|
str_res = """
|
|
diff lwr upr p adj
|
|
2 - 3 4.722222 -4.8376022 14.28205 0.4630831
|
|
1 - 3 14.722222 5.1623978 24.28205 0.0014315
|
|
1 - 2 10.000000 0.4401756 19.55982 0.0384598
|
|
"""
|
|
res_expect = np.asarray(str_res.replace(" - ", " ").split()[5:],
|
|
dtype=float).reshape((3, 6))
|
|
data = ([26, 30, 54, 25, 70, 52, 51, 26, 67,
|
|
27, 14, 29, 19, 29, 31, 41, 20, 44],
|
|
[18, 21, 29, 17, 12, 18, 35, 30, 36,
|
|
42, 26, 19, 16, 39, 28, 21, 39, 29],
|
|
[36, 21, 24, 18, 10, 43, 28, 15, 26,
|
|
20, 21, 24, 17, 13, 15, 15, 16, 28])
|
|
|
|
res_tukey = stats.tukey_hsd(*data)
|
|
conf = res_tukey.confidence_interval()
|
|
# loop over the comparisons
|
|
for i, j, s, l, h, p in res_expect:
|
|
i, j = int(i) - 1, int(j) - 1
|
|
# atols are set to the number of digits present in the r result.
|
|
assert_allclose(conf.low[i, j], l, atol=1e-7)
|
|
assert_allclose(res_tukey.statistic[i, j], s, atol=1e-6)
|
|
assert_allclose(conf.high[i, j], h, atol=1e-5)
|
|
assert_allclose(res_tukey.pvalue[i, j], p, atol=1e-7)
|
|
|
|
def test_engineering_stat_handbook(self):
|
|
'''
|
|
Example sourced from:
|
|
https://www.itl.nist.gov/div898/handbook/prc/section4/prc471.htm
|
|
'''
|
|
group1 = [6.9, 5.4, 5.8, 4.6, 4.0]
|
|
group2 = [8.3, 6.8, 7.8, 9.2, 6.5]
|
|
group3 = [8.0, 10.5, 8.1, 6.9, 9.3]
|
|
group4 = [5.8, 3.8, 6.1, 5.6, 6.2]
|
|
res = stats.tukey_hsd(group1, group2, group3, group4)
|
|
conf = res.confidence_interval()
|
|
lower = np.asarray([
|
|
[0, 0, 0, -2.25],
|
|
[.29, 0, -2.93, .13],
|
|
[1.13, 0, 0, .97],
|
|
[0, 0, 0, 0]])
|
|
upper = np.asarray([
|
|
[0, 0, 0, 1.93],
|
|
[4.47, 0, 1.25, 4.31],
|
|
[5.31, 0, 0, 5.15],
|
|
[0, 0, 0, 0]])
|
|
|
|
for (i, j) in [(1, 0), (2, 0), (0, 3), (1, 2), (2, 3)]:
|
|
assert_allclose(conf.low[i, j], lower[i, j], atol=1e-2)
|
|
assert_allclose(conf.high[i, j], upper[i, j], atol=1e-2)
|
|
|
|
def test_rand_symm(self):
|
|
# test some expected identities of the results
|
|
np.random.seed(1234)
|
|
data = np.random.rand(3, 100)
|
|
res = stats.tukey_hsd(*data)
|
|
conf = res.confidence_interval()
|
|
# the confidence intervals should be negated symmetric of each other
|
|
assert_equal(conf.low, -conf.high.T)
|
|
# the `high` and `low` center diagonals should be the same since the
|
|
# mean difference in a self comparison is 0.
|
|
assert_equal(np.diagonal(conf.high), conf.high[0, 0])
|
|
assert_equal(np.diagonal(conf.low), conf.low[0, 0])
|
|
# statistic array should be antisymmetric with zeros on the diagonal
|
|
assert_equal(res.statistic, -res.statistic.T)
|
|
assert_equal(np.diagonal(res.statistic), 0)
|
|
# p-values should be symmetric and 1 when compared to itself
|
|
assert_equal(res.pvalue, res.pvalue.T)
|
|
assert_equal(np.diagonal(res.pvalue), 1)
|
|
|
|
def test_no_inf(self):
|
|
with assert_raises(ValueError, match="...must be finite."):
|
|
stats.tukey_hsd([1, 2, 3], [2, np.inf], [6, 7, 3])
|
|
|
|
def test_is_1d(self):
|
|
with assert_raises(ValueError, match="...must be one-dimensional"):
|
|
stats.tukey_hsd([[1, 2], [2, 3]], [2, 5], [5, 23, 6])
|
|
|
|
def test_no_empty(self):
|
|
with assert_raises(ValueError, match="...must be greater than one"):
|
|
stats.tukey_hsd([], [2, 5], [4, 5, 6])
|
|
|
|
@pytest.mark.parametrize("nargs", (0, 1))
|
|
def test_not_enough_treatments(self, nargs):
|
|
with assert_raises(ValueError, match="...more than 1 treatment."):
|
|
stats.tukey_hsd(*([[23, 7, 3]] * nargs))
|
|
|
|
@pytest.mark.parametrize("cl", [-.5, 0, 1, 2])
|
|
def test_conf_level_invalid(self, cl):
|
|
with assert_raises(ValueError, match="must be between 0 and 1"):
|
|
r = stats.tukey_hsd([23, 7, 3], [3, 4], [9, 4])
|
|
r.confidence_interval(cl)
|
|
|
|
def test_2_args_ttest(self):
|
|
# that with 2 treatments the `pvalue` is equal to that of `ttest_ind`
|
|
res_tukey = stats.tukey_hsd(*self.data_diff_size[:2])
|
|
res_ttest = stats.ttest_ind(*self.data_diff_size[:2])
|
|
assert_allclose(res_ttest.pvalue, res_tukey.pvalue[0, 1])
|
|
assert_allclose(res_ttest.pvalue, res_tukey.pvalue[1, 0])
|
|
|
|
|
|
class TestPoissonMeansTest:
|
|
@pytest.mark.parametrize("c1, n1, c2, n2, p_expect", (
|
|
# example from [1], 6. Illustrative examples: Example 1
|
|
[0, 100, 3, 100, 0.0884],
|
|
[2, 100, 6, 100, 0.1749]
|
|
))
|
|
def test_paper_examples(self, c1, n1, c2, n2, p_expect):
|
|
res = stats.poisson_means_test(c1, n1, c2, n2)
|
|
assert_allclose(res.pvalue, p_expect, atol=1e-4)
|
|
|
|
@pytest.mark.parametrize("c1, n1, c2, n2, p_expect, alt, d", (
|
|
# These test cases are produced by the wrapped fortran code from the
|
|
# original authors. Using a slightly modified version of this fortran,
|
|
# found here, https://github.com/nolanbconaway/poisson-etest,
|
|
# additional tests were created.
|
|
[20, 10, 20, 10, 0.9999997568929630, 'two-sided', 0],
|
|
[10, 10, 10, 10, 0.9999998403241203, 'two-sided', 0],
|
|
[50, 15, 1, 1, 0.09920321053409643, 'two-sided', .05],
|
|
[3, 100, 20, 300, 0.12202725450896404, 'two-sided', 0],
|
|
[3, 12, 4, 20, 0.40416087318539173, 'greater', 0],
|
|
[4, 20, 3, 100, 0.008053640402974236, 'greater', 0],
|
|
# publishing paper does not include a `less` alternative,
|
|
# so it was calculated with switched argument order and
|
|
# alternative="greater"
|
|
[4, 20, 3, 10, 0.3083216325432898, 'less', 0],
|
|
[1, 1, 50, 15, 0.09322998607245102, 'less', 0]
|
|
))
|
|
def test_fortran_authors(self, c1, n1, c2, n2, p_expect, alt, d):
|
|
res = stats.poisson_means_test(c1, n1, c2, n2, alternative=alt, diff=d)
|
|
assert_allclose(res.pvalue, p_expect, atol=2e-6, rtol=1e-16)
|
|
|
|
def test_different_results(self):
|
|
# The implementation in Fortran is known to break down at higher
|
|
# counts and observations, so we expect different results. By
|
|
# inspection we can infer the p-value to be near one.
|
|
count1, count2 = 10000, 10000
|
|
nobs1, nobs2 = 10000, 10000
|
|
res = stats.poisson_means_test(count1, nobs1, count2, nobs2)
|
|
assert_allclose(res.pvalue, 1)
|
|
|
|
def test_less_than_zero_lambda_hat2(self):
|
|
# demonstrates behavior that fixes a known fault from original Fortran.
|
|
# p-value should clearly be near one.
|
|
count1, count2 = 0, 0
|
|
nobs1, nobs2 = 1, 1
|
|
res = stats.poisson_means_test(count1, nobs1, count2, nobs2)
|
|
assert_allclose(res.pvalue, 1)
|
|
|
|
def test_input_validation(self):
|
|
count1, count2 = 0, 0
|
|
nobs1, nobs2 = 1, 1
|
|
|
|
# test non-integral events
|
|
message = '`k1` and `k2` must be integers.'
|
|
with assert_raises(TypeError, match=message):
|
|
stats.poisson_means_test(.7, nobs1, count2, nobs2)
|
|
with assert_raises(TypeError, match=message):
|
|
stats.poisson_means_test(count1, nobs1, .7, nobs2)
|
|
|
|
# test negative events
|
|
message = '`k1` and `k2` must be greater than or equal to 0.'
|
|
with assert_raises(ValueError, match=message):
|
|
stats.poisson_means_test(-1, nobs1, count2, nobs2)
|
|
with assert_raises(ValueError, match=message):
|
|
stats.poisson_means_test(count1, nobs1, -1, nobs2)
|
|
|
|
# test negative sample size
|
|
message = '`n1` and `n2` must be greater than 0.'
|
|
with assert_raises(ValueError, match=message):
|
|
stats.poisson_means_test(count1, -1, count2, nobs2)
|
|
with assert_raises(ValueError, match=message):
|
|
stats.poisson_means_test(count1, nobs1, count2, -1)
|
|
|
|
# test negative difference
|
|
message = 'diff must be greater than or equal to 0.'
|
|
with assert_raises(ValueError, match=message):
|
|
stats.poisson_means_test(count1, nobs1, count2, nobs2, diff=-1)
|
|
|
|
# test invalid alternatvie
|
|
message = 'Alternative must be one of ...'
|
|
with assert_raises(ValueError, match=message):
|
|
stats.poisson_means_test(1, 2, 1, 2, alternative='error')
|
|
|
|
|
|
class TestBWSTest:
|
|
|
|
def test_bws_input_validation(self):
|
|
rng = np.random.default_rng(4571775098104213308)
|
|
|
|
x, y = rng.random(size=(2, 7))
|
|
|
|
message = '`x` and `y` must be exactly one-dimensional.'
|
|
with pytest.raises(ValueError, match=message):
|
|
stats.bws_test([x, x], [y, y])
|
|
|
|
message = '`x` and `y` must not contain NaNs.'
|
|
with pytest.raises(ValueError, match=message):
|
|
stats.bws_test([np.nan], y)
|
|
|
|
message = '`x` and `y` must be of nonzero size.'
|
|
with pytest.raises(ValueError, match=message):
|
|
stats.bws_test(x, [])
|
|
|
|
message = 'alternative` must be one of...'
|
|
with pytest.raises(ValueError, match=message):
|
|
stats.bws_test(x, y, alternative='ekki-ekki')
|
|
|
|
message = 'method` must be an instance of...'
|
|
with pytest.raises(ValueError, match=message):
|
|
stats.bws_test(x, y, method=42)
|
|
|
|
|
|
def test_against_published_reference(self):
|
|
# Test against Example 2 in bws_test Reference [1], pg 9
|
|
# https://link.springer.com/content/pdf/10.1007/BF02762032.pdf
|
|
x = [1, 2, 3, 4, 6, 7, 8]
|
|
y = [5, 9, 10, 11, 12, 13, 14]
|
|
res = stats.bws_test(x, y, alternative='two-sided')
|
|
assert_allclose(res.statistic, 5.132, atol=1e-3)
|
|
assert_equal(res.pvalue, 10/3432)
|
|
|
|
|
|
@pytest.mark.parametrize(('alternative', 'statistic', 'pvalue'),
|
|
[('two-sided', 1.7510204081633, 0.1264422777777),
|
|
('less', -1.7510204081633, 0.05754662004662),
|
|
('greater', -1.7510204081633, 0.9424533799534)])
|
|
def test_against_R(self, alternative, statistic, pvalue):
|
|
# Test against R library BWStest function bws_test
|
|
# library(BWStest)
|
|
# options(digits=16)
|
|
# x = c(...)
|
|
# y = c(...)
|
|
# bws_test(x, y, alternative='two.sided')
|
|
rng = np.random.default_rng(4571775098104213308)
|
|
x, y = rng.random(size=(2, 7))
|
|
res = stats.bws_test(x, y, alternative=alternative)
|
|
assert_allclose(res.statistic, statistic, rtol=1e-13)
|
|
assert_allclose(res.pvalue, pvalue, atol=1e-2, rtol=1e-1)
|
|
|
|
@pytest.mark.parametrize(('alternative', 'statistic', 'pvalue'),
|
|
[('two-sided', 1.142629265891, 0.2903950180801),
|
|
('less', 0.99629665877411, 0.8545660222131),
|
|
('greater', 0.99629665877411, 0.1454339777869)])
|
|
def test_against_R_imbalanced(self, alternative, statistic, pvalue):
|
|
# Test against R library BWStest function bws_test
|
|
# library(BWStest)
|
|
# options(digits=16)
|
|
# x = c(...)
|
|
# y = c(...)
|
|
# bws_test(x, y, alternative='two.sided')
|
|
rng = np.random.default_rng(5429015622386364034)
|
|
x = rng.random(size=9)
|
|
y = rng.random(size=8)
|
|
res = stats.bws_test(x, y, alternative=alternative)
|
|
assert_allclose(res.statistic, statistic, rtol=1e-13)
|
|
assert_allclose(res.pvalue, pvalue, atol=1e-2, rtol=1e-1)
|
|
|
|
def test_method(self):
|
|
# Test that `method` parameter has the desired effect
|
|
rng = np.random.default_rng(1520514347193347862)
|
|
x, y = rng.random(size=(2, 10))
|
|
|
|
rng = np.random.default_rng(1520514347193347862)
|
|
method = stats.PermutationMethod(n_resamples=10, random_state=rng)
|
|
res1 = stats.bws_test(x, y, method=method)
|
|
|
|
assert len(res1.null_distribution) == 10
|
|
|
|
rng = np.random.default_rng(1520514347193347862)
|
|
method = stats.PermutationMethod(n_resamples=10, random_state=rng)
|
|
res2 = stats.bws_test(x, y, method=method)
|
|
|
|
assert_allclose(res1.null_distribution, res2.null_distribution)
|
|
|
|
rng = np.random.default_rng(5205143471933478621)
|
|
method = stats.PermutationMethod(n_resamples=10, random_state=rng)
|
|
res3 = stats.bws_test(x, y, method=method)
|
|
|
|
assert not np.allclose(res3.null_distribution, res1.null_distribution)
|
|
|
|
def test_directions(self):
|
|
# Sanity check of the sign of the one-sided statistic
|
|
rng = np.random.default_rng(1520514347193347862)
|
|
x = rng.random(size=5)
|
|
y = x - 1
|
|
|
|
res = stats.bws_test(x, y, alternative='greater')
|
|
assert res.statistic > 0
|
|
assert_equal(res.pvalue, 1 / len(res.null_distribution))
|
|
|
|
res = stats.bws_test(x, y, alternative='less')
|
|
assert res.statistic > 0
|
|
assert_equal(res.pvalue, 1)
|
|
|
|
res = stats.bws_test(y, x, alternative='less')
|
|
assert res.statistic < 0
|
|
assert_equal(res.pvalue, 1 / len(res.null_distribution))
|
|
|
|
res = stats.bws_test(y, x, alternative='greater')
|
|
assert res.statistic < 0
|
|
assert_equal(res.pvalue, 1)
|