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from __future__ import division, print_function, absolute_import
from itertools import product
import numpy as np
import functools
import pytest
from numpy.testing import (assert_, assert_equal, assert_allclose,
assert_almost_equal) # avoid new uses
from pytest import raises as assert_raises
import scipy.stats as stats
from scipy.stats import distributions
from scipy.stats._hypotests import (epps_singleton_2samp, cramervonmises,
_cdf_cvm, cramervonmises_2samp,
_pval_cvm_2samp_exact, barnard_exact,
boschloo_exact, permutation_test,
_all_partitions_concatenated)
from scipy.stats._mannwhitneyu import mannwhitneyu, _mwu_state
import scipy.stats._bootstrap as _bootstrap
from .common_tests import check_named_results
from scipy import special
from scipy._lib._testutils import _TestPythranFunc
class TestEppsSingleton:
def test_statistic_1(self):
# first example in Goerg & Kaiser, also in original paper of
# Epps & Singleton. Note: values do not match exactly, the
# value of the interquartile range varies depending on how
# quantiles are computed
x = np.array([-0.35, 2.55, 1.73, 0.73, 0.35,
2.69, 0.46, -0.94, -0.37, 12.07])
y = np.array([-1.15, -0.15, 2.48, 3.25, 3.71,
4.29, 5.00, 7.74, 8.38, 8.60])
w, p = epps_singleton_2samp(x, y)
assert_almost_equal(w, 15.14, decimal=1)
assert_almost_equal(p, 0.00442, decimal=3)
def test_statistic_2(self):
# second example in Goerg & Kaiser, again not a perfect match
x = np.array((0, 1, 2, 2, 2, 2, 3, 3, 3, 3, 4, 5, 5, 5, 5, 6, 10,
10, 10, 10))
y = np.array((10, 4, 0, 5, 10, 10, 0, 5, 6, 7, 10, 3, 1, 7, 0, 8, 1,
5, 8, 10))
w, p = epps_singleton_2samp(x, y)
assert_allclose(w, 8.900, atol=0.001)
assert_almost_equal(p, 0.06364, decimal=3)
def test_epps_singleton_array_like(self):
np.random.seed(1234)
x, y = np.arange(30), np.arange(28)
w1, p1 = epps_singleton_2samp(list(x), list(y))
w2, p2 = epps_singleton_2samp(tuple(x), tuple(y))
w3, p3 = epps_singleton_2samp(x, y)
assert_(w1 == w2 == w3)
assert_(p1 == p2 == p3)
def test_epps_singleton_size(self):
# raise error if less than 5 elements
x, y = (1, 2, 3, 4), np.arange(10)
assert_raises(ValueError, epps_singleton_2samp, x, y)
def test_epps_singleton_nonfinite(self):
# raise error if there are non-finite values
x, y = (1, 2, 3, 4, 5, np.inf), np.arange(10)
assert_raises(ValueError, epps_singleton_2samp, x, y)
x, y = np.arange(10), (1, 2, 3, 4, 5, np.nan)
assert_raises(ValueError, epps_singleton_2samp, x, y)
def test_epps_singleton_1d_input(self):
x = np.arange(100).reshape(-1, 1)
assert_raises(ValueError, epps_singleton_2samp, x, x)
def test_names(self):
x, y = np.arange(20), np.arange(30)
res = epps_singleton_2samp(x, y)
attributes = ('statistic', 'pvalue')
check_named_results(res, attributes)
class TestCvm:
# the expected values of the cdfs are taken from Table 1 in
# Csorgo / Faraway: The Exact and Asymptotic Distribution of
# Cramér-von Mises Statistics, 1996.
def test_cdf_4(self):
assert_allclose(
_cdf_cvm([0.02983, 0.04111, 0.12331, 0.94251], 4),
[0.01, 0.05, 0.5, 0.999],
atol=1e-4)
def test_cdf_10(self):
assert_allclose(
_cdf_cvm([0.02657, 0.03830, 0.12068, 0.56643], 10),
[0.01, 0.05, 0.5, 0.975],
atol=1e-4)
def test_cdf_1000(self):
assert_allclose(
_cdf_cvm([0.02481, 0.03658, 0.11889, 1.16120], 1000),
[0.01, 0.05, 0.5, 0.999],
atol=1e-4)
def test_cdf_inf(self):
assert_allclose(
_cdf_cvm([0.02480, 0.03656, 0.11888, 1.16204]),
[0.01, 0.05, 0.5, 0.999],
atol=1e-4)
def test_cdf_support(self):
# cdf has support on [1/(12*n), n/3]
assert_equal(_cdf_cvm([1/(12*533), 533/3], 533), [0, 1])
assert_equal(_cdf_cvm([1/(12*(27 + 1)), (27 + 1)/3], 27), [0, 1])
def test_cdf_large_n(self):
# test that asymptotic cdf and cdf for large samples are close
assert_allclose(
_cdf_cvm([0.02480, 0.03656, 0.11888, 1.16204, 100], 10000),
_cdf_cvm([0.02480, 0.03656, 0.11888, 1.16204, 100]),
atol=1e-4)
def test_large_x(self):
# for large values of x and n, the series used to compute the cdf
# converges slowly.
# this leads to bug in R package goftest and MAPLE code that is
# the basis of the implemenation in scipy
# note: cdf = 1 for x >= 1000/3 and n = 1000
assert_(0.99999 < _cdf_cvm(333.3, 1000) < 1.0)
assert_(0.99999 < _cdf_cvm(333.3) < 1.0)
def test_low_p(self):
# _cdf_cvm can return values larger than 1. In that case, we just
# return a p-value of zero.
n = 12
res = cramervonmises(np.ones(n)*0.8, 'norm')
assert_(_cdf_cvm(res.statistic, n) > 1.0)
assert_equal(res.pvalue, 0)
def test_invalid_input(self):
x = np.arange(10).reshape((2, 5))
assert_raises(ValueError, cramervonmises, x, "norm")
assert_raises(ValueError, cramervonmises, [1.5], "norm")
assert_raises(ValueError, cramervonmises, (), "norm")
def test_values_R(self):
# compared against R package goftest, version 1.1.1
# goftest::cvm.test(c(-1.7, 2, 0, 1.3, 4, 0.1, 0.6), "pnorm")
res = cramervonmises([-1.7, 2, 0, 1.3, 4, 0.1, 0.6], "norm")
assert_allclose(res.statistic, 0.288156, atol=1e-6)
assert_allclose(res.pvalue, 0.1453465, atol=1e-6)
# goftest::cvm.test(c(-1.7, 2, 0, 1.3, 4, 0.1, 0.6),
# "pnorm", mean = 3, sd = 1.5)
res = cramervonmises([-1.7, 2, 0, 1.3, 4, 0.1, 0.6], "norm", (3, 1.5))
assert_allclose(res.statistic, 0.9426685, atol=1e-6)
assert_allclose(res.pvalue, 0.002026417, atol=1e-6)
# goftest::cvm.test(c(1, 2, 5, 1.4, 0.14, 11, 13, 0.9, 7.5), "pexp")
res = cramervonmises([1, 2, 5, 1.4, 0.14, 11, 13, 0.9, 7.5], "expon")
assert_allclose(res.statistic, 0.8421854, atol=1e-6)
assert_allclose(res.pvalue, 0.004433406, atol=1e-6)
def test_callable_cdf(self):
x, args = np.arange(5), (1.4, 0.7)
r1 = cramervonmises(x, distributions.expon.cdf)
r2 = cramervonmises(x, "expon")
assert_equal((r1.statistic, r1.pvalue), (r2.statistic, r2.pvalue))
r1 = cramervonmises(x, distributions.beta.cdf, args)
r2 = cramervonmises(x, "beta", args)
assert_equal((r1.statistic, r1.pvalue), (r2.statistic, r2.pvalue))
class TestMannWhitneyU:
# All magic numbers are from R wilcox.test unless otherwise specied
# https://rdrr.io/r/stats/wilcox.test.html
# --- Test Input Validation ---
def test_input_validation(self):
x = np.array([1, 2]) # generic, valid inputs
y = np.array([3, 4])
with assert_raises(ValueError, match="`x` and `y` must be of nonzero"):
mannwhitneyu([], y)
with assert_raises(ValueError, match="`x` and `y` must be of nonzero"):
mannwhitneyu(x, [])
with assert_raises(ValueError, match="`use_continuity` must be one"):
mannwhitneyu(x, y, use_continuity='ekki')
with assert_raises(ValueError, match="`alternative` must be one of"):
mannwhitneyu(x, y, alternative='ekki')
with assert_raises(ValueError, match="`axis` must be an integer"):
mannwhitneyu(x, y, axis=1.5)
with assert_raises(ValueError, match="`method` must be one of"):
mannwhitneyu(x, y, method='ekki')
def test_auto(self):
# Test that default method ('auto') chooses intended method
np.random.seed(1)
n = 8 # threshold to switch from exact to asymptotic
# both inputs are smaller than threshold; should use exact
x = np.random.rand(n-1)
y = np.random.rand(n-1)
auto = mannwhitneyu(x, y)
asymptotic = mannwhitneyu(x, y, method='asymptotic')
exact = mannwhitneyu(x, y, method='exact')
assert auto.pvalue == exact.pvalue
assert auto.pvalue != asymptotic.pvalue
# one input is smaller than threshold; should use exact
x = np.random.rand(n-1)
y = np.random.rand(n+1)
auto = mannwhitneyu(x, y)
asymptotic = mannwhitneyu(x, y, method='asymptotic')
exact = mannwhitneyu(x, y, method='exact')
assert auto.pvalue == exact.pvalue
assert auto.pvalue != asymptotic.pvalue
# other input is smaller than threshold; should use exact
auto = mannwhitneyu(y, x)
asymptotic = mannwhitneyu(x, y, method='asymptotic')
exact = mannwhitneyu(x, y, method='exact')
assert auto.pvalue == exact.pvalue
assert auto.pvalue != asymptotic.pvalue
# both inputs are larger than threshold; should use asymptotic
x = np.random.rand(n+1)
y = np.random.rand(n+1)
auto = mannwhitneyu(x, y)
asymptotic = mannwhitneyu(x, y, method='asymptotic')
exact = mannwhitneyu(x, y, method='exact')
assert auto.pvalue != exact.pvalue
assert auto.pvalue == asymptotic.pvalue
# both inputs are smaller than threshold, but there is a tie
# should use asymptotic
x = np.random.rand(n-1)
y = np.random.rand(n-1)
y[3] = x[3]
auto = mannwhitneyu(x, y)
asymptotic = mannwhitneyu(x, y, method='asymptotic')
exact = mannwhitneyu(x, y, method='exact')
assert auto.pvalue != exact.pvalue
assert auto.pvalue == asymptotic.pvalue
# --- Test Basic Functionality ---
x = [210.052110, 110.190630, 307.918612]
y = [436.08811482466416, 416.37397329768191, 179.96975939463582,
197.8118754228619, 34.038757281225756, 138.54220550921517,
128.7769351470246, 265.92721427951852, 275.6617533155341,
592.34083395416258, 448.73177590617018, 300.61495185038905,
187.97508449019588]
# This test was written for mann_whitney_u in gh-4933.
# Originally, the p-values for alternatives were swapped;
# this has been corrected and the tests have been refactored for
# compactness, but otherwise the tests are unchanged.
# R code for comparison, e.g.:
# options(digits = 16)
# x = c(210.052110, 110.190630, 307.918612)
# y = c(436.08811482466416, 416.37397329768191, 179.96975939463582,
# 197.8118754228619, 34.038757281225756, 138.54220550921517,
# 128.7769351470246, 265.92721427951852, 275.6617533155341,
# 592.34083395416258, 448.73177590617018, 300.61495185038905,
# 187.97508449019588)
# wilcox.test(x, y, alternative="g", exact=TRUE)
cases_basic = [[{"alternative": 'two-sided', "method": "asymptotic"},
(16, 0.6865041817876)],
[{"alternative": 'less', "method": "asymptotic"},
(16, 0.3432520908938)],
[{"alternative": 'greater', "method": "asymptotic"},
(16, 0.7047591913255)],
[{"alternative": 'two-sided', "method": "exact"},
(16, 0.7035714285714)],
[{"alternative": 'less', "method": "exact"},
(16, 0.3517857142857)],
[{"alternative": 'greater', "method": "exact"},
(16, 0.6946428571429)]]
@pytest.mark.parametrize(("kwds", "expected"), cases_basic)
def test_basic(self, kwds, expected):
res = mannwhitneyu(self.x, self.y, **kwds)
assert_allclose(res, expected)
cases_continuity = [[{"alternative": 'two-sided', "use_continuity": True},
(23, 0.6865041817876)],
[{"alternative": 'less', "use_continuity": True},
(23, 0.7047591913255)],
[{"alternative": 'greater', "use_continuity": True},
(23, 0.3432520908938)],
[{"alternative": 'two-sided', "use_continuity": False},
(23, 0.6377328900502)],
[{"alternative": 'less', "use_continuity": False},
(23, 0.6811335549749)],
[{"alternative": 'greater', "use_continuity": False},
(23, 0.3188664450251)]]
@pytest.mark.parametrize(("kwds", "expected"), cases_continuity)
def test_continuity(self, kwds, expected):
# When x and y are interchanged, less and greater p-values should
# swap (compare to above). This wouldn't happen if the continuity
# correction were applied in the wrong direction. Note that less and
# greater p-values do not sum to 1 when continuity correction is on,
# which is what we'd expect. Also check that results match R when
# continuity correction is turned off.
# Note that method='asymptotic' -> exact=FALSE
# and use_continuity=False -> correct=FALSE, e.g.:
# wilcox.test(x, y, alternative="t", exact=FALSE, correct=FALSE)
res = mannwhitneyu(self.y, self.x, method='asymptotic', **kwds)
assert_allclose(res, expected)
def test_tie_correct(self):
# Test tie correction against R's wilcox.test
# options(digits = 16)
# x = c(1, 2, 3, 4)
# y = c(1, 2, 3, 4, 5)
# wilcox.test(x, y, exact=FALSE)
x = [1, 2, 3, 4]
y0 = np.array([1, 2, 3, 4, 5])
dy = np.array([0, 1, 0, 1, 0])*0.01
dy2 = np.array([0, 0, 1, 0, 0])*0.01
y = [y0-0.01, y0-dy, y0-dy2, y0, y0+dy2, y0+dy, y0+0.01]
res = mannwhitneyu(x, y, axis=-1, method="asymptotic")
U_expected = [10, 9, 8.5, 8, 7.5, 7, 6]
p_expected = [1, 0.9017048037317, 0.804080657472, 0.7086240584439,
0.6197963884941, 0.5368784563079, 0.3912672792826]
assert_equal(res.statistic, U_expected)
assert_allclose(res.pvalue, p_expected)
# --- Test Exact Distribution of U ---
# These are tabulated values of the CDF of the exact distribution of
# the test statistic from pg 52 of reference [1] (Mann-Whitney Original)
pn3 = {1: [0.25, 0.5, 0.75], 2: [0.1, 0.2, 0.4, 0.6],
3: [0.05, .1, 0.2, 0.35, 0.5, 0.65]}
pn4 = {1: [0.2, 0.4, 0.6], 2: [0.067, 0.133, 0.267, 0.4, 0.6],
3: [0.028, 0.057, 0.114, 0.2, .314, 0.429, 0.571],
4: [0.014, 0.029, 0.057, 0.1, 0.171, 0.243, 0.343, 0.443, 0.557]}
pm5 = {1: [0.167, 0.333, 0.5, 0.667],
2: [0.047, 0.095, 0.19, 0.286, 0.429, 0.571],
3: [0.018, 0.036, 0.071, 0.125, 0.196, 0.286, 0.393, 0.5, 0.607],
4: [0.008, 0.016, 0.032, 0.056, 0.095, 0.143,
0.206, 0.278, 0.365, 0.452, 0.548],
5: [0.004, 0.008, 0.016, 0.028, 0.048, 0.075, 0.111,
0.155, 0.21, 0.274, 0.345, .421, 0.5, 0.579]}
pm6 = {1: [0.143, 0.286, 0.428, 0.571],
2: [0.036, 0.071, 0.143, 0.214, 0.321, 0.429, 0.571],
3: [0.012, 0.024, 0.048, 0.083, 0.131,
0.19, 0.274, 0.357, 0.452, 0.548],
4: [0.005, 0.01, 0.019, 0.033, 0.057, 0.086, 0.129,
0.176, 0.238, 0.305, 0.381, 0.457, 0.543], # the last element
# of the previous list, 0.543, has been modified from 0.545;
# I assume it was a typo
5: [0.002, 0.004, 0.009, 0.015, 0.026, 0.041, 0.063, 0.089,
0.123, 0.165, 0.214, 0.268, 0.331, 0.396, 0.465, 0.535],
6: [0.001, 0.002, 0.004, 0.008, 0.013, 0.021, 0.032, 0.047,
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))
assert_allclose(_mwu_state.cdf(k=u, m=m, n=n), 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, m=m, n=n)
+ _mwu_state.sf(k=u2, m=m, n=n)
- _mwu_state.pmf(k=u2, m=m, n=n), 1)
# check symmetry about mean of U, i.e. pmf(U) = pmf(m*n-U)
pmf = _mwu_state.pmf(k=u2, m=m, n=n)
assert_allclose(pmf, pmf[::-1])
# check symmetry w.r.t. interchange of m, n
pmf2 = _mwu_state.pmf(k=u2, m=n, n=m)
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_6897(self):
# Test for correct behavior with empty input
with assert_raises(ValueError, match="`x` and `y` must be of nonzero"):
mannwhitneyu([], [])
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)
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 'less'..."):
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)
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])
class TestCvm_2samp:
def test_invalid_input(self):
x = np.arange(10).reshape((2, 5))
y = np.arange(5)
msg = 'The samples must be one-dimensional'
with pytest.raises(ValueError, match=msg):
cramervonmises_2samp(x, y)
with pytest.raises(ValueError, match=msg):
cramervonmises_2samp(y, x)
msg = 'x and y must contain at least two observations.'
with pytest.raises(ValueError, match=msg):
cramervonmises_2samp([], y)
with pytest.raises(ValueError, match=msg):
cramervonmises_2samp(y, [1])
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)
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(10)
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 10 observations
x = np.arange(11)
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))
def test_all_partitions_concatenated():
# make sure that _all_paritions_concatenated produces the correct number
# of partitions of the data into samples of the given sizes and that
# all are unique
n = np.array([3, 2, 4], dtype=int)
nc = np.cumsum(n)
all_partitions = set()
counter = 0
for partition_concatenated in _all_partitions_concatenated(n):
counter += 1
partitioning = np.split(partition_concatenated, nc[:-1])
all_partitions.add(tuple([frozenset(i) for i in partitioning]))
expected = np.product([special.binom(sum(n[i:]), sum(n[i+1:]))
for i in range(len(n)-1)])
assert_equal(counter, expected)
assert_equal(len(all_partitions), expected)
class TestPermutationTest:
rtol = 1e-14
# -- Input validation -- #
def test_permutation_test_iv(self):
def stat(x, y, axis):
return stats.ttest_ind((x, y), axis).statistic
message = "each sample in `data` must contain two or more ..."
with pytest.raises(ValueError, match=message):
permutation_test(([1, 2, 3], [1]), stat)
message = "`data` must be a tuple containing at least two samples"
with pytest.raises(ValueError, match=message):
permutation_test((1,), stat)
with pytest.raises(TypeError, match=message):
permutation_test(1, stat)
message = "`axis` must be an integer."
with pytest.raises(ValueError, match=message):
permutation_test(([1, 2, 3], [1, 2, 3]), stat, axis=1.5)
message = "`permutation_type` must be in..."
with pytest.raises(ValueError, match=message):
permutation_test(([1, 2, 3], [1, 2, 3]), stat,
permutation_type="ekki")
message = "`vectorized` must be `True` or `False`."
with pytest.raises(ValueError, match=message):
permutation_test(([1, 2, 3], [1, 2, 3]), stat, vectorized=1.5)
message = "`n_resamples` must be a positive integer."
with pytest.raises(ValueError, match=message):
permutation_test(([1, 2, 3], [1, 2, 3]), stat, n_resamples=-1000)
message = "`n_resamples` must be a positive integer."
with pytest.raises(ValueError, match=message):
permutation_test(([1, 2, 3], [1, 2, 3]), stat, n_resamples=1000.5)
message = "`batch` must be a positive integer or None."
with pytest.raises(ValueError, match=message):
permutation_test(([1, 2, 3], [1, 2, 3]), stat, batch=-1000)
message = "`batch` must be a positive integer or None."
with pytest.raises(ValueError, match=message):
permutation_test(([1, 2, 3], [1, 2, 3]), stat, batch=1000.5)
message = "`alternative` must be in..."
with pytest.raises(ValueError, match=message):
permutation_test(([1, 2, 3], [1, 2, 3]), stat, alternative='ekki')
message = "'herring' cannot be used to seed a"
with pytest.raises(ValueError, match=message):
permutation_test(([1, 2, 3], [1, 2, 3]), stat,
random_state='herring')
# -- Test Parameters -- #
@pytest.mark.parametrize('permutation_type',
['pairings', 'samples', 'independent'])
def test_batch(self, permutation_type):
# make sure that the `batch` parameter is respected by checking the
# maximum batch size provided in calls to `statistic`
np.random.seed(0)
x = np.random.rand(10)
y = np.random.rand(10)
def statistic(x, y, axis):
batch_size = 1 if x.ndim == 1 else len(x)
statistic.batch_size = max(batch_size, statistic.batch_size)
statistic.counter += 1
return np.mean(x, axis=axis) - np.mean(y, axis=axis)
statistic.counter = 0
statistic.batch_size = 0
kwds = {'n_resamples': 1000, 'permutation_type': permutation_type,
'vectorized': True, 'random_state': 0}
res1 = stats.permutation_test((x, y), statistic, batch=1, **kwds)
assert_equal(statistic.counter, 1001)
assert_equal(statistic.batch_size, 1)
statistic.counter = 0
res2 = stats.permutation_test((x, y), statistic, batch=50, **kwds)
assert_equal(statistic.counter, 21)
assert_equal(statistic.batch_size, 50)
statistic.counter = 0
res3 = stats.permutation_test((x, y), statistic, batch=1000, **kwds)
assert_equal(statistic.counter, 2)
assert_equal(statistic.batch_size, 1000)
assert_equal(res1.pvalue, res3.pvalue)
assert_equal(res2.pvalue, res3.pvalue)
@pytest.mark.parametrize('permutation_type, exact_size',
[('pairings', special.factorial(3)**2),
('samples', 2**3),
('independent', special.binom(6, 3))])
def test_permutations(self, permutation_type, exact_size):
# make sure that the `permutations` parameter is respected by checking
# the size of the null distribution
np.random.seed(0)
x = np.random.rand(3)
y = np.random.rand(3)
def statistic(x, y, axis):
return np.mean(x, axis=axis) - np.mean(y, axis=axis)
kwds = {'permutation_type': permutation_type,
'vectorized': True, 'random_state': 0}
res = stats.permutation_test((x, y), statistic, n_resamples=3, **kwds)
assert_equal(res.null_distribution.size, 3)
res = stats.permutation_test((x, y), statistic, **kwds)
assert_equal(res.null_distribution.size, exact_size)
# -- Randomized Permutation Tests -- #
# To get reasonable accuracy, these next three tests are somewhat slow.
# Originally, I had them passing for all combinations of permutation type,
# alternative, and RNG, but that takes too long for CI. Instead, split
# into three tests, each testing a particular combination of the three
# parameters.
def test_randomized_test_against_exact_both(self):
# check that the randomized and exact tests agree to reasonable
# precision for permutation_type='both
alternative, rng = 'less', 0
nx, ny, permutations = 8, 9, 24000
assert special.binom(nx + ny, nx) > permutations
x = stats.norm.rvs(size=nx)
y = stats.norm.rvs(size=ny)
data = x, y
def statistic(x, y, axis):
return np.mean(x, axis=axis) - np.mean(y, axis=axis)
kwds = {'vectorized': True, 'permutation_type': 'independent',
'batch': 100, 'alternative': alternative, 'random_state': rng}
res = permutation_test(data, statistic, n_resamples=permutations,
**kwds)
res2 = permutation_test(data, statistic, n_resamples=np.inf, **kwds)
assert res.statistic == res2.statistic
assert_allclose(res.pvalue, res2.pvalue, atol=1e-2)
def test_randomized_test_against_exact_samples(self):
# check that the randomized and exact tests agree to reasonable
# precision for permutation_type='samples'
alternative, rng = 'greater', None
nx, ny, permutations = 15, 15, 32000
assert 2**nx > permutations
x = stats.norm.rvs(size=nx)
y = stats.norm.rvs(size=ny)
data = x, y
def statistic(x, y, axis):
return np.mean(x - y, axis=axis)
kwds = {'vectorized': True, 'permutation_type': 'samples',
'batch': 100, 'alternative': alternative, 'random_state': rng}
res = permutation_test(data, statistic, n_resamples=permutations,
**kwds)
res2 = permutation_test(data, statistic, n_resamples=np.inf, **kwds)
assert res.statistic == res2.statistic
assert_allclose(res.pvalue, res2.pvalue, atol=1e-2)
def test_randomized_test_against_exact_pairings(self):
# check that the randomized and exact tests agree to reasonable
# precision for permutation_type='pairings'
alternative = 'two-sided'
try:
rng = np.random.default_rng(1)
except AttributeError:
rng = np.random.RandomState(1)
nx, ny, permutations = 8, 8, 40000
assert special.factorial(nx) > permutations
x = stats.norm.rvs(size=nx)
y = stats.norm.rvs(size=ny)
data = [x]
def statistic1d(x):
return stats.pearsonr(x, y)[0]
statistic = _bootstrap._vectorize_statistic(statistic1d)
kwds = {'vectorized': True, 'permutation_type': 'samples',
'batch': 100, 'alternative': alternative, 'random_state': rng}
res = permutation_test(data, statistic, n_resamples=permutations,
**kwds)
res2 = permutation_test(data, statistic, n_resamples=np.inf, **kwds)
assert res.statistic == res2.statistic
assert_allclose(res.pvalue, res2.pvalue, atol=1e-2)
@pytest.mark.parametrize('alternative', ('less', 'greater'))
# Different conventions for two-sided p-value here VS ttest_ind.
# Eventually, we can add multiple options for the two-sided alternative
# here in permutation_test.
@pytest.mark.parametrize('permutations', (30, 1e9))
@pytest.mark.parametrize('axis', (0, 1, 2))
def test_against_permutation_ttest(self, alternative, permutations, axis):
# check that this function and ttest_ind with permutations give
# essentially identical results.
x = np.arange(3*4*5).reshape(3, 4, 5)
y = np.moveaxis(np.arange(4)[:, None, None], 0, axis)
res1 = stats.ttest_ind(x, y, permutations=permutations, axis=axis,
random_state=0, alternative=alternative)
def statistic(x, y, axis):
return stats.ttest_ind(x, y, axis=axis).statistic
res2 = permutation_test((x, y), statistic, vectorized=True,
n_resamples=permutations,
alternative=alternative, axis=axis,
random_state=0)
assert_allclose(res1.statistic, res2.statistic, rtol=self.rtol)
if permutations == 30:
# Even one-sided p-value is defined differently in ttest_ind for
# randomized tests. See permutation_test references [2] and [3].
assert_allclose((res1.pvalue*30+1)/31, res2.pvalue, rtol=self.rtol)
else:
assert_allclose(res1.pvalue, res2.pvalue, rtol=self.rtol)
# -- Independent (Unpaired) Sample Tests -- #
def test_against_kstest(self):
np.random.seed(0)
x = stats.norm.rvs(size=4, scale=1)
y = stats.norm.rvs(size=5, loc=3, scale=3)
alternative = 'greater'
expected = stats.ks_2samp(x, y, alternative=alternative, mode='exact')
def statistic1d(x, y):
return stats.ks_2samp(x, y, mode='asymp',
alternative=alternative).statistic
res = permutation_test((x, y), statistic1d, n_resamples=np.inf,
alternative=alternative)
assert_allclose(res.statistic, expected.statistic, rtol=self.rtol)
assert_allclose(res.pvalue, expected.pvalue, rtol=self.rtol)
@pytest.mark.parametrize('alternative', ("less", "greater", "two-sided"))
def test_against_ansari(self, alternative):
np.random.seed(0)
x = stats.norm.rvs(size=4, scale=1)
y = stats.norm.rvs(size=5, scale=3)
# ansari has a different convention for 'alternative'
alternative_correspondence = {"less": "greater",
"greater": "less",
"two-sided": "two-sided"}
alternative_scipy = alternative_correspondence[alternative]
expected = stats.ansari(x, y, alternative=alternative_scipy)
def statistic1d(x, y):
return stats.ansari(x, y).statistic
res = permutation_test((x, y), statistic1d, n_resamples=np.inf,
alternative=alternative)
assert_allclose(res.statistic, expected.statistic, rtol=self.rtol)
assert_allclose(res.pvalue, expected.pvalue, rtol=self.rtol)
@pytest.mark.parametrize('alternative', ("less", "greater", "two-sided"))
def test_against_mannwhitneyu(self, alternative):
np.random.seed(0)
x = stats.uniform.rvs(size=(3, 5, 2), loc=0)
y = stats.uniform.rvs(size=(3, 5, 2), loc=0.05)
expected = stats.mannwhitneyu(x, y, axis=1, alternative=alternative)
def statistic(x, y, axis):
return stats.mannwhitneyu(x, y, axis=axis).statistic
res = permutation_test((x, y), statistic, vectorized=True,
n_resamples=np.inf, alternative=alternative,
axis=1)
assert_allclose(res.statistic, expected.statistic, rtol=self.rtol)
assert_allclose(res.pvalue, expected.pvalue, rtol=self.rtol)
def test_against_cvm(self):
np.random.seed(0)
x = stats.norm.rvs(size=4, scale=1)
y = stats.norm.rvs(size=5, loc=3, scale=3)
expected = stats.cramervonmises_2samp(x, y, method='exact')
def statistic1d(x, y):
return stats.cramervonmises_2samp(x, y,
method='asymptotic').statistic
# cramervonmises_2samp has only one alternative, greater
res = permutation_test((x, y), statistic1d, n_resamples=np.inf,
alternative='greater')
assert_allclose(res.statistic, expected.statistic, rtol=self.rtol)
assert_allclose(res.pvalue, expected.pvalue, rtol=self.rtol)
@pytest.mark.slow()
@pytest.mark.parametrize('axis', (-1, 2))
def test_vectorized_nsamp_ptype_both(self, axis):
# Test that permutation_test with permutation_type='independent' works
# properly for a 3-sample statistic with nd array samples of different
# (but compatible) shapes and ndims. Show that exact permutation test
# and random permutation tests approximate SciPy's asymptotic pvalues
# and that exact and random permutation test results are even closer
# to one another (than they are to the asymptotic results).
np.random.seed(0)
# Three samples, different (but compatible) shapes with different ndims
x = np.random.rand(3)
y = np.random.rand(1, 3, 2)
z = np.random.rand(2, 1, 4)
data = (x, y, z)
# Define the statistic (and pvalue for comparison)
def statistic1d(*data):
return stats.kruskal(*data).statistic
def pvalue1d(*data):
return stats.kruskal(*data).pvalue
statistic = _bootstrap._vectorize_statistic(statistic1d)
pvalue = _bootstrap._vectorize_statistic(pvalue1d)
# Calculate the expected results
x2 = np.broadcast_to(x, (2, 3, 3)) # broadcast manually because
y2 = np.broadcast_to(y, (2, 3, 2)) # _vectorize_statistic doesn't
z2 = np.broadcast_to(z, (2, 3, 4))
expected_statistic = statistic(x2, y2, z2, axis=axis)
expected_pvalue = pvalue(x2, y2, z2, axis=axis)
# Calculate exact and randomized permutation results
kwds = {'vectorized': False, 'axis': axis, 'alternative': 'greater',
'permutation_type': 'independent', 'random_state': 0}
res = permutation_test(data, statistic1d, n_resamples=np.inf, **kwds)
res2 = permutation_test(data, statistic1d, n_resamples=1000, **kwds)
# Check results
assert_allclose(res.statistic, expected_statistic, rtol=self.rtol)
assert_allclose(res.statistic, res2.statistic, rtol=self.rtol)
assert_allclose(res.pvalue, expected_pvalue, atol=6e-2)
assert_allclose(res.pvalue, res2.pvalue, atol=3e-2)
# -- Paired-Sample Tests -- #
@pytest.mark.parametrize('alternative', ("less", "greater", "two-sided"))
def test_against_wilcoxon(self, alternative):
np.random.seed(0)
x = stats.uniform.rvs(size=(3, 6, 2), loc=0)
y = stats.uniform.rvs(size=(3, 6, 2), loc=0.05)
# We'll check both 1- and 2-sample versions of the same test;
# we expect identical results to wilcoxon in all cases.
def statistic_1samp_1d(z):
# 'less' ensures we get the same of two statistics every time
return stats.wilcoxon(z, alternative='less').statistic
def statistic_2samp_1d(x, y):
return stats.wilcoxon(x, y, alternative='less').statistic
def test_1d(x, y):
return stats.wilcoxon(x, y, alternative=alternative)
test = _bootstrap._vectorize_statistic(test_1d)
expected = test(x, y, axis=1)
expected_stat = expected[:, 0, :]
expected_p = expected[:, 1, :]
res1 = permutation_test((x-y,), statistic_1samp_1d, vectorized=False,
permutation_type='samples', n_resamples=np.inf,
alternative=alternative, axis=1)
res2 = permutation_test((x, y), statistic_2samp_1d, vectorized=False,
permutation_type='samples', n_resamples=np.inf,
alternative=alternative, axis=1)
# `wilcoxon` returns a different statistic with 'two-sided'
assert_allclose(res1.statistic, res2.statistic, rtol=self.rtol)
if alternative != 'two-sided':
assert_allclose(res2.statistic, expected_stat, rtol=self.rtol)
assert_allclose(res2.pvalue, expected_p, rtol=self.rtol)
assert_allclose(res1.pvalue, res2.pvalue, rtol=self.rtol)
@pytest.mark.parametrize('alternative', ("less", "greater", "two-sided"))
def test_against_binomtest(self, alternative):
np.random.seed(0)
x = np.random.randint(0, 2, size=10)
x[x == 0] = -1
# More naturally, the test would flip elements between 0 and one.
# However, permutation_test will flip the _signs_ of the elements.
# So we have to work with +1/-1 instead of 1/0.
def statistic(x, axis=0):
return np.sum(x > 0, axis=axis)
k, n, p = statistic(x), 10, 0.5
expected = stats.binomtest(k, n, p, alternative=alternative)
res = stats.permutation_test((x,), statistic, vectorized=True,
permutation_type='samples',
n_resamples=np.inf,
alternative=alternative)
assert_allclose(res.pvalue, expected.pvalue, rtol=self.rtol)
# -- Exact Association Tests -- #
def test_against_kendalltau(self):
np.random.seed(0)
x = stats.norm.rvs(size=6)
y = x + stats.norm.rvs(size=6)
expected = stats.kendalltau(x, y, method='exact')
def statistic1d(x):
return stats.kendalltau(x, y, method='asymptotic').correlation
# kendalltau currently has only one alternative, two-sided
res = permutation_test((x,), statistic1d, permutation_type='pairings',
n_resamples=np.inf)
assert_allclose(res.statistic, expected.correlation, rtol=self.rtol)
assert_allclose(res.pvalue, expected.pvalue, rtol=self.rtol)
@pytest.mark.parametrize('alternative', ('less', 'greater', 'two-sided'))
def test_against_fisher_exact(self, alternative):
def statistic(x,):
return np.sum((x == 1) & (y == 1))
np.random.seed(0)
# x and y are binary random variables with some dependence
x = (np.random.rand(7) > 0.6).astype(float)
y = (np.random.rand(7) + 0.25*x > 0.6).astype(float)
tab = stats.contingency.crosstab(x, y)[1]
res = permutation_test((x,), statistic, permutation_type='pairings',
n_resamples=np.inf, alternative=alternative)
res2 = stats.fisher_exact(tab, alternative=alternative)
assert_allclose(res.pvalue, res2[1])
@pytest.mark.slow()
@pytest.mark.parametrize('axis', (-2, 1))
def test_vectorized_nsamp_ptype_samples(self, axis):
# Test that permutation_test with permutation_type='samples' works
# properly for a 3-sample statistic with nd array samples of different
# (but compatible) shapes and ndims. Show that exact permutation test
# reproduces SciPy's exact pvalue and that random permutation test
# approximates it.
np.random.seed(0)
x = np.random.rand(2, 4, 3)
y = np.random.rand(1, 4, 3)
z = np.random.rand(2, 4, 1)
x = stats.rankdata(x, axis=axis)
y = stats.rankdata(y, axis=axis)
z = stats.rankdata(z, axis=axis)
y = y[0] # to check broadcast with different ndim
data = (x, y, z)
def statistic1d(*data):
return stats.page_trend_test(data, ranked=True,
method='asymptotic').statistic
def pvalue1d(*data):
return stats.page_trend_test(data, ranked=True,
method='exact').pvalue
statistic = _bootstrap._vectorize_statistic(statistic1d)
pvalue = _bootstrap._vectorize_statistic(pvalue1d)
expected_statistic = statistic(*np.broadcast_arrays(*data), axis=axis)
expected_pvalue = pvalue(*np.broadcast_arrays(*data), axis=axis)
kwds = {'vectorized': False, 'axis': axis, 'alternative': 'greater',
'permutation_type': 'pairings', 'random_state': 0}
res = permutation_test(data, statistic1d, n_resamples=np.inf, **kwds)
res2 = permutation_test(data, statistic1d, n_resamples=5000, **kwds)
assert_allclose(res.statistic, expected_statistic, rtol=self.rtol)
assert_allclose(res.statistic, res2.statistic, rtol=self.rtol)
assert_allclose(res.pvalue, expected_pvalue, rtol=self.rtol)
assert_allclose(res.pvalue, res2.pvalue, atol=3e-2)
# -- Test Against External References -- #
tie_case_1 = {'x': [1, 2, 3, 4], 'y': [1.5, 2, 2.5],
'expected_less': 0.2000000000,
'expected_2sided': 0.4, # 2*expected_less
'expected_Pr_gte_S_mean': 0.3428571429, # see note below
'expected_statistic': 7.5,
'expected_avg': 9.142857, 'expected_std': 1.40698}
tie_case_2 = {'x': [111, 107, 100, 99, 102, 106, 109, 108],
'y': [107, 108, 106, 98, 105, 103, 110, 105, 104],
'expected_less': 0.1555738379,
'expected_2sided': 0.3111476758,
'expected_Pr_gte_S_mean': 0.2969971205, # see note below
'expected_statistic': 32.5,
'expected_avg': 38.117647, 'expected_std': 5.172124}
@pytest.mark.slow() # only the second case is slow, really
@pytest.mark.parametrize('case', (tie_case_1, tie_case_2))
def test_with_ties(self, case):
"""
Results above from SAS PROC NPAR1WAY, e.g.
DATA myData;
INPUT X Y;
CARDS;
1 1
1 2
1 3
1 4
2 1.5
2 2
2 2.5
ods graphics on;
proc npar1way AB data=myData;
class X;
EXACT;
run;
ods graphics off;
Note: SAS provides Pr >= |S-Mean|, which is different from our
definition of a two-sided p-value.
"""
x = case['x']
y = case['y']
expected_statistic = case['expected_statistic']
expected_less = case['expected_less']
expected_2sided = case['expected_2sided']
expected_Pr_gte_S_mean = case['expected_Pr_gte_S_mean']
expected_avg = case['expected_avg']
expected_std = case['expected_std']
def statistic1d(x, y):
return stats.ansari(x, y).statistic
with np.testing.suppress_warnings() as sup:
sup.filter(UserWarning, "Ties preclude use of exact statistic")
res = permutation_test((x, y), statistic1d, n_resamples=np.inf,
alternative='less')
res2 = permutation_test((x, y), statistic1d, n_resamples=np.inf,
alternative='two-sided')
assert_allclose(res.statistic, expected_statistic, rtol=self.rtol)
assert_allclose(res.pvalue, expected_less, atol=1e-10)
assert_allclose(res2.pvalue, expected_2sided, atol=1e-10)
assert_allclose(res2.null_distribution.mean(), expected_avg, rtol=1e-6)
assert_allclose(res2.null_distribution.std(), expected_std, rtol=1e-6)
# SAS provides Pr >= |S-Mean|; might as well check against that, too
S = res.statistic
mean = res.null_distribution.mean()
n = len(res.null_distribution)
Pr_gte_S_mean = np.sum(np.abs(res.null_distribution-mean)
>= np.abs(S-mean))/n
assert_allclose(expected_Pr_gte_S_mean, Pr_gte_S_mean)
@pytest.mark.parametrize('alternative, expected_pvalue',
(('less', 0.9708333333333),
('greater', 0.05138888888889),
('two-sided', 0.1027777777778)))
def test_against_spearmanr_in_R(self, alternative, expected_pvalue):
"""
Results above from R cor.test, e.g.
options(digits=16)
x <- c(1.76405235, 0.40015721, 0.97873798,
2.2408932, 1.86755799, -0.97727788)
y <- c(2.71414076, 0.2488, 0.87551913,
2.6514917, 2.01160156, 0.47699563)
cor.test(x, y, method = "spearm", alternative = "t")
"""
np.random.seed(0)
x = stats.norm.rvs(size=6)
y = x + stats.norm.rvs(size=6)
expected_statistic = 0.7714285714285715
def statistic1d(x):
return stats.spearmanr(x, y).correlation
res = permutation_test((x,), statistic1d, permutation_type='pairings',
n_resamples=np.inf, alternative=alternative)
assert_allclose(res.statistic, expected_statistic, rtol=self.rtol)
assert_allclose(res.pvalue, expected_pvalue, atol=1e-13)
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])
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