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_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_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_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_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_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)
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))
