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))
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_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 raise an error. No nan_policy for now.
y[4] = np.nan
with assert_raises(ValueError, match="`x` and `y` must not contain"):
mannwhitneyu(x, y)
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))
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_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
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_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)
def test_gh_4067(self):
# Test for correct behavior with all NaN input
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])
with assert_raises(ValueError, match="`x` and `y` must not contain"):
mannwhitneyu(a, b)
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_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)
def test_scalar_data(self, kwds, result):
# just making sure scalars work
assert_allclose(mannwhitneyu(1, 2, **kwds), result)
def test_basic(self, kwds, expected):
res = mannwhitneyu(self.x, self.y, **kwds)
assert_allclose(res, expected)
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
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="`x` and `y` must not contain"):
mannwhitneyu([np.nan, 2], y)
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')