# Author: Travis Oliphant, 2002 # # Further enhancements and tests added by numerous SciPy developers. # from __future__ import division, print_function, absolute_import import warnings import numpy as np from numpy.random import RandomState from numpy.testing import (assert_array_equal, assert_almost_equal, assert_array_less, assert_array_almost_equal, assert_, assert_allclose, assert_equal, assert_warns) import pytest from pytest import raises as assert_raises from scipy._lib._numpy_compat import suppress_warnings from scipy import stats from .common_tests import check_named_results # Matplotlib is not a scipy dependency but is optionally used in probplot, so # check if it's available try: import matplotlib.pyplot as plt have_matplotlib = True except Exception: have_matplotlib = False # test data gear.dat from NIST for Levene and Bartlett test # https://www.itl.nist.gov/div898/handbook/eda/section3/eda3581.htm g1 = [1.006, 0.996, 0.998, 1.000, 0.992, 0.993, 1.002, 0.999, 0.994, 1.000] g2 = [0.998, 1.006, 1.000, 1.002, 0.997, 0.998, 0.996, 1.000, 1.006, 0.988] g3 = [0.991, 0.987, 0.997, 0.999, 0.995, 0.994, 1.000, 0.999, 0.996, 0.996] g4 = [1.005, 1.002, 0.994, 1.000, 0.995, 0.994, 0.998, 0.996, 1.002, 0.996] g5 = [0.998, 0.998, 0.982, 0.990, 1.002, 0.984, 0.996, 0.993, 0.980, 0.996] g6 = [1.009, 1.013, 1.009, 0.997, 0.988, 1.002, 0.995, 0.998, 0.981, 0.996] g7 = [0.990, 1.004, 0.996, 1.001, 0.998, 1.000, 1.018, 1.010, 0.996, 1.002] g8 = [0.998, 1.000, 1.006, 1.000, 1.002, 0.996, 0.998, 0.996, 1.002, 1.006] g9 = [1.002, 0.998, 0.996, 0.995, 0.996, 1.004, 1.004, 0.998, 0.999, 0.991] g10 = [0.991, 0.995, 0.984, 0.994, 0.997, 0.997, 0.991, 0.998, 1.004, 0.997] class TestBayes_mvs(object): def test_basic(self): # Expected values in this test simply taken from the function. For # some checks regarding correctness of implementation, see review in # gh-674 data = [6, 9, 12, 7, 8, 8, 13] mean, var, std = stats.bayes_mvs(data) assert_almost_equal(mean.statistic, 9.0) assert_allclose(mean.minmax, (7.1036502226125329, 10.896349777387467), rtol=1e-14) assert_almost_equal(var.statistic, 10.0) assert_allclose(var.minmax, (3.1767242068607087, 24.45910381334018), rtol=1e-09) assert_almost_equal(std.statistic, 2.9724954732045084, decimal=14) assert_allclose(std.minmax, (1.7823367265645145, 4.9456146050146312), rtol=1e-14) def test_empty_input(self): assert_raises(ValueError, stats.bayes_mvs, []) def test_result_attributes(self): x = np.arange(15) attributes = ('statistic', 'minmax') res = stats.bayes_mvs(x) for i in res: check_named_results(i, attributes) class TestMvsdist(object): def test_basic(self): data = [6, 9, 12, 7, 8, 8, 13] mean, var, std = stats.mvsdist(data) assert_almost_equal(mean.mean(), 9.0) assert_allclose(mean.interval(0.9), (7.1036502226125329, 10.896349777387467), rtol=1e-14) assert_almost_equal(var.mean(), 10.0) assert_allclose(var.interval(0.9), (3.1767242068607087, 24.45910381334018), rtol=1e-09) assert_almost_equal(std.mean(), 2.9724954732045084, decimal=14) assert_allclose(std.interval(0.9), (1.7823367265645145, 4.9456146050146312), rtol=1e-14) def test_empty_input(self): assert_raises(ValueError, stats.mvsdist, []) def test_bad_arg(self): # Raise ValueError if fewer than two data points are given. data = [1] assert_raises(ValueError, stats.mvsdist, data) def test_warns(self): # regression test for gh-5270 # make sure there are no spurious divide-by-zero warnings with warnings.catch_warnings(): warnings.simplefilter('error', RuntimeWarning) [x.mean() for x in stats.mvsdist([1, 2, 3])] [x.mean() for x in stats.mvsdist([1, 2, 3, 4, 5])] class TestShapiro(object): def test_basic(self): x1 = [0.11, 7.87, 4.61, 10.14, 7.95, 3.14, 0.46, 4.43, 0.21, 4.75, 0.71, 1.52, 3.24, 0.93, 0.42, 4.97, 9.53, 4.55, 0.47, 6.66] w, pw = stats.shapiro(x1) assert_almost_equal(w, 0.90047299861907959, 6) assert_almost_equal(pw, 0.042089745402336121, 6) x2 = [1.36, 1.14, 2.92, 2.55, 1.46, 1.06, 5.27, -1.11, 3.48, 1.10, 0.88, -0.51, 1.46, 0.52, 6.20, 1.69, 0.08, 3.67, 2.81, 3.49] w, pw = stats.shapiro(x2) assert_almost_equal(w, 0.9590270, 6) assert_almost_equal(pw, 0.52460, 3) # Verified against R np.random.seed(12345678) x3 = stats.norm.rvs(loc=5, scale=3, size=100) w, pw = stats.shapiro(x3) assert_almost_equal(w, 0.9772805571556091, decimal=6) assert_almost_equal(pw, 0.08144091814756393, decimal=3) # Extracted from original paper x4 = [0.139, 0.157, 0.175, 0.256, 0.344, 0.413, 0.503, 0.577, 0.614, 0.655, 0.954, 1.392, 1.557, 1.648, 1.690, 1.994, 2.174, 2.206, 3.245, 3.510, 3.571, 4.354, 4.980, 6.084, 8.351] W_expected = 0.83467 p_expected = 0.000914 w, pw = stats.shapiro(x4) assert_almost_equal(w, W_expected, decimal=4) assert_almost_equal(pw, p_expected, decimal=5) def test_2d(self): x1 = [[0.11, 7.87, 4.61, 10.14, 7.95, 3.14, 0.46, 4.43, 0.21, 4.75], [0.71, 1.52, 3.24, 0.93, 0.42, 4.97, 9.53, 4.55, 0.47, 6.66]] w, pw = stats.shapiro(x1) assert_almost_equal(w, 0.90047299861907959, 6) assert_almost_equal(pw, 0.042089745402336121, 6) x2 = [[1.36, 1.14, 2.92, 2.55, 1.46, 1.06, 5.27, -1.11, 3.48, 1.10], [0.88, -0.51, 1.46, 0.52, 6.20, 1.69, 0.08, 3.67, 2.81, 3.49]] w, pw = stats.shapiro(x2) assert_almost_equal(w, 0.9590270, 6) assert_almost_equal(pw, 0.52460, 3) def test_empty_input(self): assert_raises(ValueError, stats.shapiro, []) assert_raises(ValueError, stats.shapiro, [[], [], []]) def test_not_enough_values(self): assert_raises(ValueError, stats.shapiro, [1, 2]) assert_raises(ValueError, stats.shapiro, [[], [2]]) def test_bad_arg(self): # Length of x is less than 3. x = [1] assert_raises(ValueError, stats.shapiro, x) def test_nan_input(self): x = np.arange(10.) x[9] = np.nan w, pw = stats.shapiro(x) assert_equal(w, np.nan) assert_almost_equal(pw, 1.0) class TestAnderson(object): def test_normal(self): rs = RandomState(1234567890) x1 = rs.standard_exponential(size=50) x2 = rs.standard_normal(size=50) A, crit, sig = stats.anderson(x1) assert_array_less(crit[:-1], A) A, crit, sig = stats.anderson(x2) assert_array_less(A, crit[-2:]) v = np.ones(10) v[0] = 0 A, crit, sig = stats.anderson(v) # The expected statistic 3.208057 was computed independently of scipy. # For example, in R: # > library(nortest) # > v <- rep(1, 10) # > v[1] <- 0 # > result <- ad.test(v) # > result$statistic # A # 3.208057 assert_allclose(A, 3.208057) def test_expon(self): rs = RandomState(1234567890) x1 = rs.standard_exponential(size=50) x2 = rs.standard_normal(size=50) A, crit, sig = stats.anderson(x1, 'expon') assert_array_less(A, crit[-2:]) olderr = np.seterr(all='ignore') try: A, crit, sig = stats.anderson(x2, 'expon') finally: np.seterr(**olderr) assert_(A > crit[-1]) def test_gumbel(self): # Regression test for gh-6306. Before that issue was fixed, # this case would return a2=inf. v = np.ones(100) v[0] = 0.0 a2, crit, sig = stats.anderson(v, 'gumbel') # A brief reimplementation of the calculation of the statistic. n = len(v) xbar, s = stats.gumbel_l.fit(v) logcdf = stats.gumbel_l.logcdf(v, xbar, s) logsf = stats.gumbel_l.logsf(v, xbar, s) i = np.arange(1, n+1) expected_a2 = -n - np.mean((2*i - 1) * (logcdf + logsf[::-1])) assert_allclose(a2, expected_a2) def test_bad_arg(self): assert_raises(ValueError, stats.anderson, [1], dist='plate_of_shrimp') def test_result_attributes(self): rs = RandomState(1234567890) x = rs.standard_exponential(size=50) res = stats.anderson(x) attributes = ('statistic', 'critical_values', 'significance_level') check_named_results(res, attributes) def test_gumbel_l(self): # gh-2592, gh-6337 # Adds support to 'gumbel_r' and 'gumbel_l' as valid inputs for dist. rs = RandomState(1234567890) x = rs.gumbel(size=100) A1, crit1, sig1 = stats.anderson(x, 'gumbel') A2, crit2, sig2 = stats.anderson(x, 'gumbel_l') assert_allclose(A2, A1) def test_gumbel_r(self): # gh-2592, gh-6337 # Adds support to 'gumbel_r' and 'gumbel_l' as valid inputs for dist. rs = RandomState(1234567890) x1 = rs.gumbel(size=100) x2 = np.ones(100) A1, crit1, sig1 = stats.anderson(x1, 'gumbel_r') A2, crit2, sig2 = stats.anderson(x2, 'gumbel_r') assert_array_less(A1, crit1[-2:]) assert_(A2 > crit2[-1]) class TestAndersonKSamp(object): def test_example1a(self): # Example data from Scholz & Stephens (1987), originally # published in Lehmann (1995, Nonparametrics, Statistical # Methods Based on Ranks, p. 309) # Pass a mixture of lists and arrays t1 = [38.7, 41.5, 43.8, 44.5, 45.5, 46.0, 47.7, 58.0] t2 = np.array([39.2, 39.3, 39.7, 41.4, 41.8, 42.9, 43.3, 45.8]) t3 = np.array([34.0, 35.0, 39.0, 40.0, 43.0, 43.0, 44.0, 45.0]) t4 = np.array([34.0, 34.8, 34.8, 35.4, 37.2, 37.8, 41.2, 42.8]) Tk, tm, p = stats.anderson_ksamp((t1, t2, t3, t4), midrank=False) assert_almost_equal(Tk, 4.449, 3) assert_array_almost_equal([0.4985, 1.3237, 1.9158, 2.4930, 3.2459], tm[0:5], 4) assert_allclose(p, 0.0021, atol=0.00025) def test_example1b(self): # Example data from Scholz & Stephens (1987), originally # published in Lehmann (1995, Nonparametrics, Statistical # Methods Based on Ranks, p. 309) # Pass arrays t1 = np.array([38.7, 41.5, 43.8, 44.5, 45.5, 46.0, 47.7, 58.0]) t2 = np.array([39.2, 39.3, 39.7, 41.4, 41.8, 42.9, 43.3, 45.8]) t3 = np.array([34.0, 35.0, 39.0, 40.0, 43.0, 43.0, 44.0, 45.0]) t4 = np.array([34.0, 34.8, 34.8, 35.4, 37.2, 37.8, 41.2, 42.8]) Tk, tm, p = stats.anderson_ksamp((t1, t2, t3, t4), midrank=True) assert_almost_equal(Tk, 4.480, 3) assert_array_almost_equal([0.4985, 1.3237, 1.9158, 2.4930, 3.2459], tm[0:5], 4) assert_allclose(p, 0.0020, atol=0.00025) def test_example2a(self): # Example data taken from an earlier technical report of # Scholz and Stephens # Pass lists instead of arrays t1 = [194, 15, 41, 29, 33, 181] t2 = [413, 14, 58, 37, 100, 65, 9, 169, 447, 184, 36, 201, 118] t3 = [34, 31, 18, 18, 67, 57, 62, 7, 22, 34] t4 = [90, 10, 60, 186, 61, 49, 14, 24, 56, 20, 79, 84, 44, 59, 29, 118, 25, 156, 310, 76, 26, 44, 23, 62] t5 = [130, 208, 70, 101, 208] t6 = [74, 57, 48, 29, 502, 12, 70, 21, 29, 386, 59, 27] t7 = [55, 320, 56, 104, 220, 239, 47, 246, 176, 182, 33] t8 = [23, 261, 87, 7, 120, 14, 62, 47, 225, 71, 246, 21, 42, 20, 5, 12, 120, 11, 3, 14, 71, 11, 14, 11, 16, 90, 1, 16, 52, 95] t9 = [97, 51, 11, 4, 141, 18, 142, 68, 77, 80, 1, 16, 106, 206, 82, 54, 31, 216, 46, 111, 39, 63, 18, 191, 18, 163, 24] t10 = [50, 44, 102, 72, 22, 39, 3, 15, 197, 188, 79, 88, 46, 5, 5, 36, 22, 139, 210, 97, 30, 23, 13, 14] t11 = [359, 9, 12, 270, 603, 3, 104, 2, 438] t12 = [50, 254, 5, 283, 35, 12] t13 = [487, 18, 100, 7, 98, 5, 85, 91, 43, 230, 3, 130] t14 = [102, 209, 14, 57, 54, 32, 67, 59, 134, 152, 27, 14, 230, 66, 61, 34] Tk, tm, p = stats.anderson_ksamp((t1, t2, t3, t4, t5, t6, t7, t8, t9, t10, t11, t12, t13, t14), midrank=False) assert_almost_equal(Tk, 3.288, 3) assert_array_almost_equal([0.5990, 1.3269, 1.8052, 2.2486, 2.8009], tm[0:5], 4) assert_allclose(p, 0.0041, atol=0.00025) def test_example2b(self): # Example data taken from an earlier technical report of # Scholz and Stephens t1 = [194, 15, 41, 29, 33, 181] t2 = [413, 14, 58, 37, 100, 65, 9, 169, 447, 184, 36, 201, 118] t3 = [34, 31, 18, 18, 67, 57, 62, 7, 22, 34] t4 = [90, 10, 60, 186, 61, 49, 14, 24, 56, 20, 79, 84, 44, 59, 29, 118, 25, 156, 310, 76, 26, 44, 23, 62] t5 = [130, 208, 70, 101, 208] t6 = [74, 57, 48, 29, 502, 12, 70, 21, 29, 386, 59, 27] t7 = [55, 320, 56, 104, 220, 239, 47, 246, 176, 182, 33] t8 = [23, 261, 87, 7, 120, 14, 62, 47, 225, 71, 246, 21, 42, 20, 5, 12, 120, 11, 3, 14, 71, 11, 14, 11, 16, 90, 1, 16, 52, 95] t9 = [97, 51, 11, 4, 141, 18, 142, 68, 77, 80, 1, 16, 106, 206, 82, 54, 31, 216, 46, 111, 39, 63, 18, 191, 18, 163, 24] t10 = [50, 44, 102, 72, 22, 39, 3, 15, 197, 188, 79, 88, 46, 5, 5, 36, 22, 139, 210, 97, 30, 23, 13, 14] t11 = [359, 9, 12, 270, 603, 3, 104, 2, 438] t12 = [50, 254, 5, 283, 35, 12] t13 = [487, 18, 100, 7, 98, 5, 85, 91, 43, 230, 3, 130] t14 = [102, 209, 14, 57, 54, 32, 67, 59, 134, 152, 27, 14, 230, 66, 61, 34] Tk, tm, p = stats.anderson_ksamp((t1, t2, t3, t4, t5, t6, t7, t8, t9, t10, t11, t12, t13, t14), midrank=True) assert_almost_equal(Tk, 3.294, 3) assert_array_almost_equal([0.5990, 1.3269, 1.8052, 2.2486, 2.8009], tm[0:5], 4) assert_allclose(p, 0.0041, atol=0.00025) def test_R_kSamples(self): # test values generates with R package kSamples # package version 1.2-6 (2017-06-14) # r1 = 1:100 # continuous case (no ties) --> version 1 # res <- kSamples::ad.test(r1, r1 + 40.5) # res$ad[1, "T.AD"] # 41.105 # res$ad[1, " asympt. P-value"] # 5.8399e-18 # # discrete case (ties allowed) --> version 2 (here: midrank=True) # res$ad[2, "T.AD"] # 41.235 # # res <- kSamples::ad.test(r1, r1 + .5) # res$ad[1, "T.AD"] # -1.2824 # res$ad[1, " asympt. P-value"] # 1 # res$ad[2, "T.AD"] # -1.2944 # # res <- kSamples::ad.test(r1, r1 + 7.5) # res$ad[1, "T.AD"] # 1.4923 # res$ad[1, " asympt. P-value"] # 0.077501 # # res <- kSamples::ad.test(r1, r1 + 6) # res$ad[2, "T.AD"] # 0.63892 # res$ad[2, " asympt. P-value"] # 0.17981 # # res <- kSamples::ad.test(r1, r1 + 11.5) # res$ad[1, "T.AD"] # 4.5042 # res$ad[1, " asympt. P-value"] # 0.00545 # # res <- kSamples::ad.test(r1, r1 + 13.5) # res$ad[1, "T.AD"] # 6.2982 # res$ad[1, " asympt. P-value"] # 0.00118 x1 = np.linspace(1, 100, 100) # test case: different distributions;p-value floored at 0.001 # test case for issue #5493 / #8536 with suppress_warnings() as sup: sup.filter(UserWarning, message='p-value floored') s, _, p = stats.anderson_ksamp([x1, x1 + 40.5], midrank=False) assert_almost_equal(s, 41.105, 3) assert_equal(p, 0.001) with suppress_warnings() as sup: sup.filter(UserWarning, message='p-value floored') s, _, p = stats.anderson_ksamp([x1, x1 + 40.5]) assert_almost_equal(s, 41.235, 3) assert_equal(p, 0.001) # test case: similar distributions --> p-value capped at 0.25 with suppress_warnings() as sup: sup.filter(UserWarning, message='p-value capped') s, _, p = stats.anderson_ksamp([x1, x1 + .5], midrank=False) assert_almost_equal(s, -1.2824, 4) assert_equal(p, 0.25) with suppress_warnings() as sup: sup.filter(UserWarning, message='p-value capped') s, _, p = stats.anderson_ksamp([x1, x1 + .5]) assert_almost_equal(s, -1.2944, 4) assert_equal(p, 0.25) # test case: check interpolated p-value in [0.01, 0.25] (no ties) s, _, p = stats.anderson_ksamp([x1, x1 + 7.5], midrank=False) assert_almost_equal(s, 1.4923, 4) assert_allclose(p, 0.0775, atol=0.005, rtol=0) # test case: check interpolated p-value in [0.01, 0.25] (w/ ties) s, _, p = stats.anderson_ksamp([x1, x1 + 6]) assert_almost_equal(s, 0.6389, 4) assert_allclose(p, 0.1798, atol=0.005, rtol=0) # test extended critical values for p=0.001 and p=0.005 s, _, p = stats.anderson_ksamp([x1, x1 + 11.5], midrank=False) assert_almost_equal(s, 4.5042, 4) assert_allclose(p, 0.00545, atol=0.0005, rtol=0) s, _, p = stats.anderson_ksamp([x1, x1 + 13.5], midrank=False) assert_almost_equal(s, 6.2982, 4) assert_allclose(p, 0.00118, atol=0.0001, rtol=0) def test_not_enough_samples(self): assert_raises(ValueError, stats.anderson_ksamp, np.ones(5)) def test_no_distinct_observations(self): assert_raises(ValueError, stats.anderson_ksamp, (np.ones(5), np.ones(5))) def test_empty_sample(self): assert_raises(ValueError, stats.anderson_ksamp, (np.ones(5), [])) def test_result_attributes(self): # Pass a mixture of lists and arrays t1 = [38.7, 41.5, 43.8, 44.5, 45.5, 46.0, 47.7, 58.0] t2 = np.array([39.2, 39.3, 39.7, 41.4, 41.8, 42.9, 43.3, 45.8]) res = stats.anderson_ksamp((t1, t2), midrank=False) attributes = ('statistic', 'critical_values', 'significance_level') check_named_results(res, attributes) class TestAnsari(object): def test_small(self): x = [1, 2, 3, 3, 4] y = [3, 2, 6, 1, 6, 1, 4, 1] with suppress_warnings() as sup: sup.filter(UserWarning, "Ties preclude use of exact statistic.") W, pval = stats.ansari(x, y) assert_almost_equal(W, 23.5, 11) assert_almost_equal(pval, 0.13499256881897437, 11) def test_approx(self): ramsay = np.array((111, 107, 100, 99, 102, 106, 109, 108, 104, 99, 101, 96, 97, 102, 107, 113, 116, 113, 110, 98)) parekh = np.array((107, 108, 106, 98, 105, 103, 110, 105, 104, 100, 96, 108, 103, 104, 114, 114, 113, 108, 106, 99)) with suppress_warnings() as sup: sup.filter(UserWarning, "Ties preclude use of exact statistic.") W, pval = stats.ansari(ramsay, parekh) assert_almost_equal(W, 185.5, 11) assert_almost_equal(pval, 0.18145819972867083, 11) def test_exact(self): W, pval = stats.ansari([1, 2, 3, 4], [15, 5, 20, 8, 10, 12]) assert_almost_equal(W, 10.0, 11) assert_almost_equal(pval, 0.533333333333333333, 7) def test_bad_arg(self): assert_raises(ValueError, stats.ansari, [], [1]) assert_raises(ValueError, stats.ansari, [1], []) def test_result_attributes(self): x = [1, 2, 3, 3, 4] y = [3, 2, 6, 1, 6, 1, 4, 1] with suppress_warnings() as sup: sup.filter(UserWarning, "Ties preclude use of exact statistic.") res = stats.ansari(x, y) attributes = ('statistic', 'pvalue') check_named_results(res, attributes) class TestBartlett(object): def test_data(self): # https://www.itl.nist.gov/div898/handbook/eda/section3/eda357.htm args = [g1, g2, g3, g4, g5, g6, g7, g8, g9, g10] T, pval = stats.bartlett(*args) assert_almost_equal(T, 20.78587342806484, 7) assert_almost_equal(pval, 0.0136358632781, 7) def test_bad_arg(self): # Too few args raises ValueError. assert_raises(ValueError, stats.bartlett, [1]) def test_result_attributes(self): args = [g1, g2, g3, g4, g5, g6, g7, g8, g9, g10] res = stats.bartlett(*args) attributes = ('statistic', 'pvalue') check_named_results(res, attributes) def test_empty_arg(self): args = (g1, g2, g3, g4, g5, g6, g7, g8, g9, g10, []) assert_equal((np.nan, np.nan), stats.bartlett(*args)) # temporary fix for issue #9252: only accept 1d input def test_1d_input(self): x = np.array([[1, 2], [3, 4]]) assert_raises(ValueError, stats.bartlett, g1, x) class TestLevene(object): def test_data(self): # https://www.itl.nist.gov/div898/handbook/eda/section3/eda35a.htm args = [g1, g2, g3, g4, g5, g6, g7, g8, g9, g10] W, pval = stats.levene(*args) assert_almost_equal(W, 1.7059176930008939, 7) assert_almost_equal(pval, 0.0990829755522, 7) def test_trimmed1(self): # Test that center='trimmed' gives the same result as center='mean' # when proportiontocut=0. W1, pval1 = stats.levene(g1, g2, g3, center='mean') W2, pval2 = stats.levene(g1, g2, g3, center='trimmed', proportiontocut=0.0) assert_almost_equal(W1, W2) assert_almost_equal(pval1, pval2) def test_trimmed2(self): x = [1.2, 2.0, 3.0, 4.0, 5.0, 6.0, 7.0, 100.0] y = [0.0, 3.0, 3.5, 4.0, 4.5, 5.0, 5.5, 200.0] np.random.seed(1234) x2 = np.random.permutation(x) # Use center='trimmed' W0, pval0 = stats.levene(x, y, center='trimmed', proportiontocut=0.125) W1, pval1 = stats.levene(x2, y, center='trimmed', proportiontocut=0.125) # Trim the data here, and use center='mean' W2, pval2 = stats.levene(x[1:-1], y[1:-1], center='mean') # Result should be the same. assert_almost_equal(W0, W2) assert_almost_equal(W1, W2) assert_almost_equal(pval1, pval2) def test_equal_mean_median(self): x = np.linspace(-1, 1, 21) np.random.seed(1234) x2 = np.random.permutation(x) y = x**3 W1, pval1 = stats.levene(x, y, center='mean') W2, pval2 = stats.levene(x2, y, center='median') assert_almost_equal(W1, W2) assert_almost_equal(pval1, pval2) def test_bad_keyword(self): x = np.linspace(-1, 1, 21) assert_raises(TypeError, stats.levene, x, x, portiontocut=0.1) def test_bad_center_value(self): x = np.linspace(-1, 1, 21) assert_raises(ValueError, stats.levene, x, x, center='trim') def test_too_few_args(self): assert_raises(ValueError, stats.levene, [1]) def test_result_attributes(self): args = [g1, g2, g3, g4, g5, g6, g7, g8, g9, g10] res = stats.levene(*args) attributes = ('statistic', 'pvalue') check_named_results(res, attributes) # temporary fix for issue #9252: only accept 1d input def test_1d_input(self): x = np.array([[1, 2], [3, 4]]) assert_raises(ValueError, stats.levene, g1, x) class TestBinomP(object): def test_data(self): pval = stats.binom_test(100, 250) assert_almost_equal(pval, 0.0018833009350757682, 11) pval = stats.binom_test(201, 405) assert_almost_equal(pval, 0.92085205962670713, 11) pval = stats.binom_test([682, 243], p=3.0/4) assert_almost_equal(pval, 0.38249155957481695, 11) def test_bad_len_x(self): # Length of x must be 1 or 2. assert_raises(ValueError, stats.binom_test, [1, 2, 3]) def test_bad_n(self): # len(x) is 1, but n is invalid. # Missing n assert_raises(ValueError, stats.binom_test, [100]) # n less than x[0] assert_raises(ValueError, stats.binom_test, [100], n=50) def test_bad_p(self): assert_raises(ValueError, stats.binom_test, [50, 50], p=2.0) def test_alternatives(self): res = stats.binom_test(51, 235, p=1./6, alternative='less') assert_almost_equal(res, 0.982022657605858) res = stats.binom_test(51, 235, p=1./6, alternative='greater') assert_almost_equal(res, 0.02654424571169085) res = stats.binom_test(51, 235, p=1./6, alternative='two-sided') assert_almost_equal(res, 0.0437479701823997) class TestFligner(object): def test_data(self): # numbers from R: fligner.test in package stats x1 = np.arange(5) assert_array_almost_equal(stats.fligner(x1, x1**2), (3.2282229927203536, 0.072379187848207877), 11) def test_trimmed1(self): # Perturb input to break ties in the transformed data # See https://github.com/scipy/scipy/pull/8042 for more details rs = np.random.RandomState(123) _perturb = lambda g: (np.asarray(g) + 1e-10*rs.randn(len(g))).tolist() g1_ = _perturb(g1) g2_ = _perturb(g2) g3_ = _perturb(g3) # Test that center='trimmed' gives the same result as center='mean' # when proportiontocut=0. Xsq1, pval1 = stats.fligner(g1_, g2_, g3_, center='mean') Xsq2, pval2 = stats.fligner(g1_, g2_, g3_, center='trimmed', proportiontocut=0.0) assert_almost_equal(Xsq1, Xsq2) assert_almost_equal(pval1, pval2) def test_trimmed2(self): x = [1.2, 2.0, 3.0, 4.0, 5.0, 6.0, 7.0, 100.0] y = [0.0, 3.0, 3.5, 4.0, 4.5, 5.0, 5.5, 200.0] # Use center='trimmed' Xsq1, pval1 = stats.fligner(x, y, center='trimmed', proportiontocut=0.125) # Trim the data here, and use center='mean' Xsq2, pval2 = stats.fligner(x[1:-1], y[1:-1], center='mean') # Result should be the same. assert_almost_equal(Xsq1, Xsq2) assert_almost_equal(pval1, pval2) # The following test looks reasonable at first, but fligner() uses the # function stats.rankdata(), and in one of the cases in this test, # there are ties, while in the other (because of normal rounding # errors) there are not. This difference leads to differences in the # third significant digit of W. # #def test_equal_mean_median(self): # x = np.linspace(-1,1,21) # y = x**3 # W1, pval1 = stats.fligner(x, y, center='mean') # W2, pval2 = stats.fligner(x, y, center='median') # assert_almost_equal(W1, W2) # assert_almost_equal(pval1, pval2) def test_bad_keyword(self): x = np.linspace(-1, 1, 21) assert_raises(TypeError, stats.fligner, x, x, portiontocut=0.1) def test_bad_center_value(self): x = np.linspace(-1, 1, 21) assert_raises(ValueError, stats.fligner, x, x, center='trim') def test_bad_num_args(self): # Too few args raises ValueError. assert_raises(ValueError, stats.fligner, [1]) def test_empty_arg(self): x = np.arange(5) assert_equal((np.nan, np.nan), stats.fligner(x, x**2, [])) class TestMood(object): def test_mood(self): # numbers from R: mood.test in package stats x1 = np.arange(5) assert_array_almost_equal(stats.mood(x1, x1**2), (-1.3830857299399906, 0.16663858066771478), 11) def test_mood_order_of_args(self): # z should change sign when the order of arguments changes, pvalue # should not change np.random.seed(1234) x1 = np.random.randn(10, 1) x2 = np.random.randn(15, 1) z1, p1 = stats.mood(x1, x2) z2, p2 = stats.mood(x2, x1) assert_array_almost_equal([z1, p1], [-z2, p2]) def test_mood_with_axis_none(self): # Test with axis = None, compare with results from R x1 = [-0.626453810742332, 0.183643324222082, -0.835628612410047, 1.59528080213779, 0.329507771815361, -0.820468384118015, 0.487429052428485, 0.738324705129217, 0.575781351653492, -0.305388387156356, 1.51178116845085, 0.389843236411431, -0.621240580541804, -2.2146998871775, 1.12493091814311, -0.0449336090152309, -0.0161902630989461, 0.943836210685299, 0.821221195098089, 0.593901321217509] x2 = [-0.896914546624981, 0.184849184646742, 1.58784533120882, -1.13037567424629, -0.0802517565509893, 0.132420284381094, 0.707954729271733, -0.23969802417184, 1.98447393665293, -0.138787012119665, 0.417650750792556, 0.981752777463662, -0.392695355503813, -1.03966897694891, 1.78222896030858, -2.31106908460517, 0.878604580921265, 0.035806718015226, 1.01282869212708, 0.432265154539617, 2.09081920524915, -1.19992581964387, 1.58963820029007, 1.95465164222325, 0.00493777682814261, -2.45170638784613, 0.477237302613617, -0.596558168631403, 0.792203270299649, 0.289636710177348] x1 = np.array(x1) x2 = np.array(x2) x1.shape = (10, 2) x2.shape = (15, 2) assert_array_almost_equal(stats.mood(x1, x2, axis=None), [-1.31716607555, 0.18778296257]) def test_mood_2d(self): # Test if the results of mood test in 2-D case are consistent with the # R result for the same inputs. Numbers from R mood.test(). ny = 5 np.random.seed(1234) x1 = np.random.randn(10, ny) x2 = np.random.randn(15, ny) z_vectest, pval_vectest = stats.mood(x1, x2) for j in range(ny): assert_array_almost_equal([z_vectest[j], pval_vectest[j]], stats.mood(x1[:, j], x2[:, j])) # inverse order of dimensions x1 = x1.transpose() x2 = x2.transpose() z_vectest, pval_vectest = stats.mood(x1, x2, axis=1) for i in range(ny): # check axis handling is self consistent assert_array_almost_equal([z_vectest[i], pval_vectest[i]], stats.mood(x1[i, :], x2[i, :])) def test_mood_3d(self): shape = (10, 5, 6) np.random.seed(1234) x1 = np.random.randn(*shape) x2 = np.random.randn(*shape) for axis in range(3): z_vectest, pval_vectest = stats.mood(x1, x2, axis=axis) # Tests that result for 3-D arrays is equal to that for the # same calculation on a set of 1-D arrays taken from the # 3-D array axes_idx = ([1, 2], [0, 2], [0, 1]) # the two axes != axis for i in range(shape[axes_idx[axis][0]]): for j in range(shape[axes_idx[axis][1]]): if axis == 0: slice1 = x1[:, i, j] slice2 = x2[:, i, j] elif axis == 1: slice1 = x1[i, :, j] slice2 = x2[i, :, j] else: slice1 = x1[i, j, :] slice2 = x2[i, j, :] assert_array_almost_equal([z_vectest[i, j], pval_vectest[i, j]], stats.mood(slice1, slice2)) def test_mood_bad_arg(self): # Raise ValueError when the sum of the lengths of the args is # less than 3 assert_raises(ValueError, stats.mood, [1], []) class TestProbplot(object): def test_basic(self): np.random.seed(12345) x = stats.norm.rvs(size=20) osm, osr = stats.probplot(x, fit=False) osm_expected = [-1.8241636, -1.38768012, -1.11829229, -0.91222575, -0.73908135, -0.5857176, -0.44506467, -0.31273668, -0.18568928, -0.06158146, 0.06158146, 0.18568928, 0.31273668, 0.44506467, 0.5857176, 0.73908135, 0.91222575, 1.11829229, 1.38768012, 1.8241636] assert_allclose(osr, np.sort(x)) assert_allclose(osm, osm_expected) res, res_fit = stats.probplot(x, fit=True) res_fit_expected = [1.05361841, 0.31297795, 0.98741609] assert_allclose(res_fit, res_fit_expected) def test_sparams_keyword(self): np.random.seed(123456) x = stats.norm.rvs(size=100) # Check that None, () and 0 (loc=0, for normal distribution) all work # and give the same results osm1, osr1 = stats.probplot(x, sparams=None, fit=False) osm2, osr2 = stats.probplot(x, sparams=0, fit=False) osm3, osr3 = stats.probplot(x, sparams=(), fit=False) assert_allclose(osm1, osm2) assert_allclose(osm1, osm3) assert_allclose(osr1, osr2) assert_allclose(osr1, osr3) # Check giving (loc, scale) params for normal distribution osm, osr = stats.probplot(x, sparams=(), fit=False) def test_dist_keyword(self): np.random.seed(12345) x = stats.norm.rvs(size=20) osm1, osr1 = stats.probplot(x, fit=False, dist='t', sparams=(3,)) osm2, osr2 = stats.probplot(x, fit=False, dist=stats.t, sparams=(3,)) assert_allclose(osm1, osm2) assert_allclose(osr1, osr2) assert_raises(ValueError, stats.probplot, x, dist='wrong-dist-name') assert_raises(AttributeError, stats.probplot, x, dist=[]) class custom_dist(object): """Some class that looks just enough like a distribution.""" def ppf(self, q): return stats.norm.ppf(q, loc=2) osm1, osr1 = stats.probplot(x, sparams=(2,), fit=False) osm2, osr2 = stats.probplot(x, dist=custom_dist(), fit=False) assert_allclose(osm1, osm2) assert_allclose(osr1, osr2) @pytest.mark.skipif(not have_matplotlib, reason="no matplotlib") def test_plot_kwarg(self): np.random.seed(7654321) fig = plt.figure() fig.add_subplot(111) x = stats.t.rvs(3, size=100) res1, fitres1 = stats.probplot(x, plot=plt) plt.close() res2, fitres2 = stats.probplot(x, plot=None) res3 = stats.probplot(x, fit=False, plot=plt) plt.close() res4 = stats.probplot(x, fit=False, plot=None) # Check that results are consistent between combinations of `fit` and # `plot` keywords. assert_(len(res1) == len(res2) == len(res3) == len(res4) == 2) assert_allclose(res1, res2) assert_allclose(res1, res3) assert_allclose(res1, res4) assert_allclose(fitres1, fitres2) # Check that a Matplotlib Axes object is accepted fig = plt.figure() ax = fig.add_subplot(111) stats.probplot(x, fit=False, plot=ax) plt.close() def test_probplot_bad_args(self): # Raise ValueError when given an invalid distribution. assert_raises(ValueError, stats.probplot, [1], dist="plate_of_shrimp") def test_empty(self): assert_equal(stats.probplot([], fit=False), (np.array([]), np.array([]))) assert_equal(stats.probplot([], fit=True), ((np.array([]), np.array([])), (np.nan, np.nan, 0.0))) def test_array_of_size_one(self): with np.errstate(invalid='ignore'): assert_equal(stats.probplot([1], fit=True), ((np.array([0.]), np.array([1])), (np.nan, np.nan, 0.0))) def test_wilcoxon_bad_arg(): # Raise ValueError when two args of different lengths are given or # zero_method is unknown. assert_raises(ValueError, stats.wilcoxon, [1], [1, 2]) assert_raises(ValueError, stats.wilcoxon, [1, 2], [1, 2], "dummy") def test_wilcoxon_arg_type(): # Should be able to accept list as arguments. # Address issue 6070. arr = [1, 2, 3, 0, -1, 3, 1, 2, 1, 1, 2] _ = stats.wilcoxon(arr, zero_method="pratt") _ = stats.wilcoxon(arr, zero_method="zsplit") _ = stats.wilcoxon(arr, zero_method="wilcox") class TestKstat(object): def test_moments_normal_distribution(self): np.random.seed(32149) data = np.random.randn(12345) moments = [] for n in [1, 2, 3, 4]: moments.append(stats.kstat(data, n)) expected = [0.011315, 1.017931, 0.05811052, 0.0754134] assert_allclose(moments, expected, rtol=1e-4) # test equivalence with `stats.moment` m1 = stats.moment(data, moment=1) m2 = stats.moment(data, moment=2) m3 = stats.moment(data, moment=3) assert_allclose((m1, m2, m3), expected[:-1], atol=0.02, rtol=1e-2) def test_empty_input(self): assert_raises(ValueError, stats.kstat, []) def test_nan_input(self): data = np.arange(10.) data[6] = np.nan assert_equal(stats.kstat(data), np.nan) def test_kstat_bad_arg(self): # Raise ValueError if n > 4 or n < 1. data = np.arange(10) for n in [0, 4.001]: assert_raises(ValueError, stats.kstat, data, n=n) class TestKstatVar(object): def test_empty_input(self): assert_raises(ValueError, stats.kstatvar, []) def test_nan_input(self): data = np.arange(10.) data[6] = np.nan assert_equal(stats.kstat(data), np.nan) def test_bad_arg(self): # Raise ValueError is n is not 1 or 2. data = [1] n = 10 assert_raises(ValueError, stats.kstatvar, data, n=n) class TestPpccPlot(object): def setup_method(self): np.random.seed(7654321) self.x = stats.loggamma.rvs(5, size=500) + 5 def test_basic(self): N = 5 svals, ppcc = stats.ppcc_plot(self.x, -10, 10, N=N) ppcc_expected = [0.21139644, 0.21384059, 0.98766719, 0.97980182, 0.93519298] assert_allclose(svals, np.linspace(-10, 10, num=N)) assert_allclose(ppcc, ppcc_expected) def test_dist(self): # Test that we can specify distributions both by name and as objects. svals1, ppcc1 = stats.ppcc_plot(self.x, -10, 10, dist='tukeylambda') svals2, ppcc2 = stats.ppcc_plot(self.x, -10, 10, dist=stats.tukeylambda) assert_allclose(svals1, svals2, rtol=1e-20) assert_allclose(ppcc1, ppcc2, rtol=1e-20) # Test that 'tukeylambda' is the default dist svals3, ppcc3 = stats.ppcc_plot(self.x, -10, 10) assert_allclose(svals1, svals3, rtol=1e-20) assert_allclose(ppcc1, ppcc3, rtol=1e-20) @pytest.mark.skipif(not have_matplotlib, reason="no matplotlib") def test_plot_kwarg(self): # Check with the matplotlib.pyplot module fig = plt.figure() ax = fig.add_subplot(111) stats.ppcc_plot(self.x, -20, 20, plot=plt) fig.delaxes(ax) # Check that a Matplotlib Axes object is accepted ax = fig.add_subplot(111) stats.ppcc_plot(self.x, -20, 20, plot=ax) plt.close() def test_invalid_inputs(self): # `b` has to be larger than `a` assert_raises(ValueError, stats.ppcc_plot, self.x, 1, 0) # Raise ValueError when given an invalid distribution. assert_raises(ValueError, stats.ppcc_plot, [1, 2, 3], 0, 1, dist="plate_of_shrimp") def test_empty(self): # For consistency with probplot return for one empty array, # ppcc contains all zeros and svals is the same as for normal array # input. svals, ppcc = stats.ppcc_plot([], 0, 1) assert_allclose(svals, np.linspace(0, 1, num=80)) assert_allclose(ppcc, np.zeros(80, dtype=float)) class TestPpccMax(object): def test_ppcc_max_bad_arg(self): # Raise ValueError when given an invalid distribution. data = [1] assert_raises(ValueError, stats.ppcc_max, data, dist="plate_of_shrimp") def test_ppcc_max_basic(self): np.random.seed(1234567) x = stats.tukeylambda.rvs(-0.7, loc=2, scale=0.5, size=10000) + 1e4 # On Python 2.6 the result is accurate to 5 decimals. On Python >= 2.7 # it is accurate up to 16 decimals assert_almost_equal(stats.ppcc_max(x), -0.71215366521264145, decimal=5) def test_dist(self): np.random.seed(1234567) x = stats.tukeylambda.rvs(-0.7, loc=2, scale=0.5, size=10000) + 1e4 # Test that we can specify distributions both by name and as objects. max1 = stats.ppcc_max(x, dist='tukeylambda') max2 = stats.ppcc_max(x, dist=stats.tukeylambda) assert_almost_equal(max1, -0.71215366521264145, decimal=5) assert_almost_equal(max2, -0.71215366521264145, decimal=5) # Test that 'tukeylambda' is the default dist max3 = stats.ppcc_max(x) assert_almost_equal(max3, -0.71215366521264145, decimal=5) def test_brack(self): np.random.seed(1234567) x = stats.tukeylambda.rvs(-0.7, loc=2, scale=0.5, size=10000) + 1e4 assert_raises(ValueError, stats.ppcc_max, x, brack=(0.0, 1.0, 0.5)) # On Python 2.6 the result is accurate to 5 decimals. On Python >= 2.7 # it is accurate up to 16 decimals assert_almost_equal(stats.ppcc_max(x, brack=(0, 1)), -0.71215366521264145, decimal=5) # On Python 2.6 the result is accurate to 5 decimals. On Python >= 2.7 # it is accurate up to 16 decimals assert_almost_equal(stats.ppcc_max(x, brack=(-2, 2)), -0.71215366521264145, decimal=5) class TestBoxcox_llf(object): def test_basic(self): np.random.seed(54321) x = stats.norm.rvs(size=10000, loc=10) lmbda = 1 llf = stats.boxcox_llf(lmbda, x) llf_expected = -x.size / 2. * np.log(np.sum(x.std()**2)) assert_allclose(llf, llf_expected) def test_array_like(self): np.random.seed(54321) x = stats.norm.rvs(size=100, loc=10) lmbda = 1 llf = stats.boxcox_llf(lmbda, x) llf2 = stats.boxcox_llf(lmbda, list(x)) assert_allclose(llf, llf2, rtol=1e-12) def test_2d_input(self): # Note: boxcox_llf() was already working with 2-D input (sort of), so # keep it like that. boxcox() doesn't work with 2-D input though, due # to brent() returning a scalar. np.random.seed(54321) x = stats.norm.rvs(size=100, loc=10) lmbda = 1 llf = stats.boxcox_llf(lmbda, x) llf2 = stats.boxcox_llf(lmbda, np.vstack([x, x]).T) assert_allclose([llf, llf], llf2, rtol=1e-12) def test_empty(self): assert_(np.isnan(stats.boxcox_llf(1, []))) class TestBoxcox(object): def test_fixed_lmbda(self): np.random.seed(12345) x = stats.loggamma.rvs(5, size=50) + 5 xt = stats.boxcox(x, lmbda=1) assert_allclose(xt, x - 1) xt = stats.boxcox(x, lmbda=-1) assert_allclose(xt, 1 - 1/x) xt = stats.boxcox(x, lmbda=0) assert_allclose(xt, np.log(x)) # Also test that array_like input works xt = stats.boxcox(list(x), lmbda=0) assert_allclose(xt, np.log(x)) def test_lmbda_None(self): np.random.seed(1234567) # Start from normal rv's, do inverse transform to check that # optimization function gets close to the right answer. np.random.seed(1245) lmbda = 2.5 x = stats.norm.rvs(loc=10, size=50000) x_inv = (x * lmbda + 1)**(-lmbda) xt, maxlog = stats.boxcox(x_inv) assert_almost_equal(maxlog, -1 / lmbda, decimal=2) def test_alpha(self): np.random.seed(1234) x = stats.loggamma.rvs(5, size=50) + 5 # Some regular values for alpha, on a small sample size _, _, interval = stats.boxcox(x, alpha=0.75) assert_allclose(interval, [4.004485780226041, 5.138756355035744]) _, _, interval = stats.boxcox(x, alpha=0.05) assert_allclose(interval, [1.2138178554857557, 8.209033272375663]) # Try some extreme values, see we don't hit the N=500 limit x = stats.loggamma.rvs(7, size=500) + 15 _, _, interval = stats.boxcox(x, alpha=0.001) assert_allclose(interval, [0.3988867, 11.40553131]) _, _, interval = stats.boxcox(x, alpha=0.999) assert_allclose(interval, [5.83316246, 5.83735292]) def test_boxcox_bad_arg(self): # Raise ValueError if any data value is negative. x = np.array([-1]) assert_raises(ValueError, stats.boxcox, x) def test_empty(self): assert_(stats.boxcox([]).shape == (0,)) class TestBoxcoxNormmax(object): def setup_method(self): np.random.seed(12345) self.x = stats.loggamma.rvs(5, size=50) + 5 def test_pearsonr(self): maxlog = stats.boxcox_normmax(self.x) assert_allclose(maxlog, 1.804465, rtol=1e-6) def test_mle(self): maxlog = stats.boxcox_normmax(self.x, method='mle') assert_allclose(maxlog, 1.758101, rtol=1e-6) # Check that boxcox() uses 'mle' _, maxlog_boxcox = stats.boxcox(self.x) assert_allclose(maxlog_boxcox, maxlog) def test_all(self): maxlog_all = stats.boxcox_normmax(self.x, method='all') assert_allclose(maxlog_all, [1.804465, 1.758101], rtol=1e-6) class TestBoxcoxNormplot(object): def setup_method(self): np.random.seed(7654321) self.x = stats.loggamma.rvs(5, size=500) + 5 def test_basic(self): N = 5 lmbdas, ppcc = stats.boxcox_normplot(self.x, -10, 10, N=N) ppcc_expected = [0.57783375, 0.83610988, 0.97524311, 0.99756057, 0.95843297] assert_allclose(lmbdas, np.linspace(-10, 10, num=N)) assert_allclose(ppcc, ppcc_expected) @pytest.mark.skipif(not have_matplotlib, reason="no matplotlib") def test_plot_kwarg(self): # Check with the matplotlib.pyplot module fig = plt.figure() ax = fig.add_subplot(111) stats.boxcox_normplot(self.x, -20, 20, plot=plt) fig.delaxes(ax) # Check that a Matplotlib Axes object is accepted ax = fig.add_subplot(111) stats.boxcox_normplot(self.x, -20, 20, plot=ax) plt.close() def test_invalid_inputs(self): # `lb` has to be larger than `la` assert_raises(ValueError, stats.boxcox_normplot, self.x, 1, 0) # `x` can not contain negative values assert_raises(ValueError, stats.boxcox_normplot, [-1, 1], 0, 1) def test_empty(self): assert_(stats.boxcox_normplot([], 0, 1).size == 0) class TestYeojohnson_llf(object): def test_array_like(self): np.random.seed(54321) x = stats.norm.rvs(size=100, loc=0) lmbda = 1 llf = stats.yeojohnson_llf(lmbda, x) llf2 = stats.yeojohnson_llf(lmbda, list(x)) assert_allclose(llf, llf2, rtol=1e-12) def test_2d_input(self): np.random.seed(54321) x = stats.norm.rvs(size=100, loc=10) lmbda = 1 llf = stats.yeojohnson_llf(lmbda, x) llf2 = stats.yeojohnson_llf(lmbda, np.vstack([x, x]).T) assert_allclose([llf, llf], llf2, rtol=1e-12) def test_empty(self): assert_(np.isnan(stats.yeojohnson_llf(1, []))) class TestYeojohnson(object): def test_fixed_lmbda(self): np.random.seed(12345) # Test positive input x = stats.loggamma.rvs(5, size=50) + 5 assert np.all(x > 0) xt = stats.yeojohnson(x, lmbda=1) assert_allclose(xt, x) xt = stats.yeojohnson(x, lmbda=-1) assert_allclose(xt, 1 - 1 / (x + 1)) xt = stats.yeojohnson(x, lmbda=0) assert_allclose(xt, np.log(x + 1)) xt = stats.yeojohnson(x, lmbda=1) assert_allclose(xt, x) # Test negative input x = stats.loggamma.rvs(5, size=50) - 5 assert np.all(x < 0) xt = stats.yeojohnson(x, lmbda=2) assert_allclose(xt, -np.log(-x + 1)) xt = stats.yeojohnson(x, lmbda=1) assert_allclose(xt, x) xt = stats.yeojohnson(x, lmbda=3) assert_allclose(xt, 1 / (-x + 1) - 1) # test both positive and negative input x = stats.loggamma.rvs(5, size=50) - 2 assert not np.all(x < 0) assert not np.all(x >= 0) pos = x >= 0 xt = stats.yeojohnson(x, lmbda=1) assert_allclose(xt[pos], x[pos]) xt = stats.yeojohnson(x, lmbda=-1) assert_allclose(xt[pos], 1 - 1 / (x[pos] + 1)) xt = stats.yeojohnson(x, lmbda=0) assert_allclose(xt[pos], np.log(x[pos] + 1)) xt = stats.yeojohnson(x, lmbda=1) assert_allclose(xt[pos], x[pos]) neg = ~pos xt = stats.yeojohnson(x, lmbda=2) assert_allclose(xt[neg], -np.log(-x[neg] + 1)) xt = stats.yeojohnson(x, lmbda=1) assert_allclose(xt[neg], x[neg]) xt = stats.yeojohnson(x, lmbda=3) assert_allclose(xt[neg], 1 / (-x[neg] + 1) - 1) @pytest.mark.parametrize('lmbda', [0, .1, .5, 2]) def test_lmbda_None(self, lmbda): # Start from normal rv's, do inverse transform to check that # optimization function gets close to the right answer. def _inverse_transform(x, lmbda): x_inv = np.zeros(x.shape, dtype=x.dtype) pos = x >= 0 # when x >= 0 if abs(lmbda) < np.spacing(1.): x_inv[pos] = np.exp(x[pos]) - 1 else: # lmbda != 0 x_inv[pos] = np.power(x[pos] * lmbda + 1, 1 / lmbda) - 1 # when x < 0 if abs(lmbda - 2) > np.spacing(1.): x_inv[~pos] = 1 - np.power(-(2 - lmbda) * x[~pos] + 1, 1 / (2 - lmbda)) else: # lmbda == 2 x_inv[~pos] = 1 - np.exp(-x[~pos]) return x_inv np.random.seed(1234567) n_samples = 20000 x = np.random.normal(loc=0, scale=1, size=(n_samples)) x_inv = _inverse_transform(x, lmbda) xt, maxlog = stats.yeojohnson(x_inv) assert_allclose(maxlog, lmbda, atol=1e-2) assert_almost_equal(0, np.linalg.norm(x - xt) / n_samples, decimal=2) assert_almost_equal(0, xt.mean(), decimal=1) assert_almost_equal(1, xt.std(), decimal=1) def test_empty(self): assert_(stats.yeojohnson([]).shape == (0,)) def test_array_like(self): np.random.seed(54321) x = stats.norm.rvs(size=100, loc=0) lmbda = 1.5 xt1, _ = stats.yeojohnson(x) xt2, _ = stats.yeojohnson(list(x)) assert_allclose(xt1, xt2, rtol=1e-12) class TestYeojohnsonNormmax(object): def setup_method(self): np.random.seed(12345) self.x = stats.loggamma.rvs(5, size=50) + 5 def test_mle(self): maxlog = stats.yeojohnson_normmax(self.x) assert_allclose(maxlog, 1.876393, rtol=1e-6) def test_darwin_example(self): # test from original paper "A new family of power transformations to # improve normality or symmetry" by Yeo and Johnson. x = [6.1, -8.4, 1.0, 2.0, 0.7, 2.9, 3.5, 5.1, 1.8, 3.6, 7.0, 3.0, 9.3, 7.5, -6.0] lmbda = stats.yeojohnson_normmax(x) assert np.allclose(lmbda, 1.305, atol=1e-3) class TestCircFuncs(object): def test_circfuncs(self): x = np.array([355, 5, 2, 359, 10, 350]) M = stats.circmean(x, high=360) Mval = 0.167690146 assert_allclose(M, Mval, rtol=1e-7) V = stats.circvar(x, high=360) Vval = 42.51955609 assert_allclose(V, Vval, rtol=1e-7) S = stats.circstd(x, high=360) Sval = 6.520702116 assert_allclose(S, Sval, rtol=1e-7) def test_circfuncs_small(self): x = np.array([20, 21, 22, 18, 19, 20.5, 19.2]) M1 = x.mean() M2 = stats.circmean(x, high=360) assert_allclose(M2, M1, rtol=1e-5) V1 = x.var() V2 = stats.circvar(x, high=360) assert_allclose(V2, V1, rtol=1e-4) S1 = x.std() S2 = stats.circstd(x, high=360) assert_allclose(S2, S1, rtol=1e-4) def test_circmean_axis(self): x = np.array([[355, 5, 2, 359, 10, 350], [351, 7, 4, 352, 9, 349], [357, 9, 8, 358, 4, 356]]) M1 = stats.circmean(x, high=360) M2 = stats.circmean(x.ravel(), high=360) assert_allclose(M1, M2, rtol=1e-14) M1 = stats.circmean(x, high=360, axis=1) M2 = [stats.circmean(x[i], high=360) for i in range(x.shape[0])] assert_allclose(M1, M2, rtol=1e-14) M1 = stats.circmean(x, high=360, axis=0) M2 = [stats.circmean(x[:, i], high=360) for i in range(x.shape[1])] assert_allclose(M1, M2, rtol=1e-14) def test_circvar_axis(self): x = np.array([[355, 5, 2, 359, 10, 350], [351, 7, 4, 352, 9, 349], [357, 9, 8, 358, 4, 356]]) V1 = stats.circvar(x, high=360) V2 = stats.circvar(x.ravel(), high=360) assert_allclose(V1, V2, rtol=1e-11) V1 = stats.circvar(x, high=360, axis=1) V2 = [stats.circvar(x[i], high=360) for i in range(x.shape[0])] assert_allclose(V1, V2, rtol=1e-11) V1 = stats.circvar(x, high=360, axis=0) V2 = [stats.circvar(x[:, i], high=360) for i in range(x.shape[1])] assert_allclose(V1, V2, rtol=1e-11) def test_circstd_axis(self): x = np.array([[355, 5, 2, 359, 10, 350], [351, 7, 4, 352, 9, 349], [357, 9, 8, 358, 4, 356]]) S1 = stats.circstd(x, high=360) S2 = stats.circstd(x.ravel(), high=360) assert_allclose(S1, S2, rtol=1e-11) S1 = stats.circstd(x, high=360, axis=1) S2 = [stats.circstd(x[i], high=360) for i in range(x.shape[0])] assert_allclose(S1, S2, rtol=1e-11) S1 = stats.circstd(x, high=360, axis=0) S2 = [stats.circstd(x[:, i], high=360) for i in range(x.shape[1])] assert_allclose(S1, S2, rtol=1e-11) def test_circfuncs_array_like(self): x = [355, 5, 2, 359, 10, 350] assert_allclose(stats.circmean(x, high=360), 0.167690146, rtol=1e-7) assert_allclose(stats.circvar(x, high=360), 42.51955609, rtol=1e-7) assert_allclose(stats.circstd(x, high=360), 6.520702116, rtol=1e-7) def test_empty(self): assert_(np.isnan(stats.circmean([]))) assert_(np.isnan(stats.circstd([]))) assert_(np.isnan(stats.circvar([]))) def test_circmean_scalar(self): x = 1. M1 = x M2 = stats.circmean(x) assert_allclose(M2, M1, rtol=1e-5) def test_circmean_range(self): # regression test for gh-6420: circmean(..., high, low) must be # between `high` and `low` m = stats.circmean(np.arange(0, 2, 0.1), np.pi, -np.pi) assert_(m < np.pi) assert_(m > -np.pi) def test_circfuncs_unit8(self): # regression test for gh-7255: overflow when working with # numpy uint8 data type x = np.array([150, 10], dtype='uint8') assert_equal(stats.circmean(x, high=180), 170.0) assert_allclose(stats.circvar(x, high=180), 437.45871686, rtol=1e-7) assert_allclose(stats.circstd(x, high=180), 20.91551378, rtol=1e-7) def test_accuracy_wilcoxon(): freq = [1, 4, 16, 15, 8, 4, 5, 1, 2] nums = range(-4, 5) x = np.concatenate([[u] * v for u, v in zip(nums, freq)]) y = np.zeros(x.size) T, p = stats.wilcoxon(x, y, "pratt") assert_allclose(T, 423) assert_allclose(p, 0.00197547303533107) T, p = stats.wilcoxon(x, y, "zsplit") assert_allclose(T, 441) assert_allclose(p, 0.0032145343172473055) T, p = stats.wilcoxon(x, y, "wilcox") assert_allclose(T, 327) assert_allclose(p, 0.00641346115861) # Test the 'correction' option, using values computed in R with: # > wilcox.test(x, y, paired=TRUE, exact=FALSE, correct={FALSE,TRUE}) x = np.array([120, 114, 181, 188, 180, 146, 121, 191, 132, 113, 127, 112]) y = np.array([133, 143, 119, 189, 112, 199, 198, 113, 115, 121, 142, 187]) T, p = stats.wilcoxon(x, y, correction=False) assert_equal(T, 34) assert_allclose(p, 0.6948866, rtol=1e-6) T, p = stats.wilcoxon(x, y, correction=True) assert_equal(T, 34) assert_allclose(p, 0.7240817, rtol=1e-6) def test_wilcoxon_result_attributes(): x = np.array([120, 114, 181, 188, 180, 146, 121, 191, 132, 113, 127, 112]) y = np.array([133, 143, 119, 189, 112, 199, 198, 113, 115, 121, 142, 187]) res = stats.wilcoxon(x, y, correction=False) attributes = ('statistic', 'pvalue') check_named_results(res, attributes) def test_wilcoxon_tie(): # Regression test for gh-2391. # Corresponding R code is: # > result = wilcox.test(rep(0.1, 10), exact=FALSE, correct=FALSE) # > result$p.value # [1] 0.001565402 # > result = wilcox.test(rep(0.1, 10), exact=FALSE, correct=TRUE) # > result$p.value # [1] 0.001904195 stat, p = stats.wilcoxon([0.1] * 10) expected_p = 0.001565402 assert_equal(stat, 0) assert_allclose(p, expected_p, rtol=1e-6) stat, p = stats.wilcoxon([0.1] * 10, correction=True) expected_p = 0.001904195 assert_equal(stat, 0) assert_allclose(p, expected_p, rtol=1e-6) class TestMedianTest(object): def test_bad_n_samples(self): # median_test requires at least two samples. assert_raises(ValueError, stats.median_test, [1, 2, 3]) def test_empty_sample(self): # Each sample must contain at least one value. assert_raises(ValueError, stats.median_test, [], [1, 2, 3]) def test_empty_when_ties_ignored(self): # The grand median is 1, and all values in the first argument are # equal to the grand median. With ties="ignore", those values are # ignored, which results in the first sample being (in effect) empty. # This should raise a ValueError. assert_raises(ValueError, stats.median_test, [1, 1, 1, 1], [2, 0, 1], [2, 0], ties="ignore") def test_empty_contingency_row(self): # The grand median is 1, and with the default ties="below", all the # values in the samples are counted as being below the grand median. # This would result a row of zeros in the contingency table, which is # an error. assert_raises(ValueError, stats.median_test, [1, 1, 1], [1, 1, 1]) # With ties="above", all the values are counted as above the # grand median. assert_raises(ValueError, stats.median_test, [1, 1, 1], [1, 1, 1], ties="above") def test_bad_ties(self): assert_raises(ValueError, stats.median_test, [1, 2, 3], [4, 5], ties="foo") def test_bad_nan_policy(self): assert_raises(ValueError, stats.median_test, [1, 2, 3], [4, 5], nan_policy='foobar') def test_bad_keyword(self): assert_raises(TypeError, stats.median_test, [1, 2, 3], [4, 5], foo="foo") def test_simple(self): x = [1, 2, 3] y = [1, 2, 3] stat, p, med, tbl = stats.median_test(x, y) # The median is floating point, but this equality test should be safe. assert_equal(med, 2.0) assert_array_equal(tbl, [[1, 1], [2, 2]]) # The expected values of the contingency table equal the contingency # table, so the statistic should be 0 and the p-value should be 1. assert_equal(stat, 0) assert_equal(p, 1) def test_ties_options(self): # Test the contingency table calculation. x = [1, 2, 3, 4] y = [5, 6] z = [7, 8, 9] # grand median is 5. # Default 'ties' option is "below". stat, p, m, tbl = stats.median_test(x, y, z) assert_equal(m, 5) assert_equal(tbl, [[0, 1, 3], [4, 1, 0]]) stat, p, m, tbl = stats.median_test(x, y, z, ties="ignore") assert_equal(m, 5) assert_equal(tbl, [[0, 1, 3], [4, 0, 0]]) stat, p, m, tbl = stats.median_test(x, y, z, ties="above") assert_equal(m, 5) assert_equal(tbl, [[0, 2, 3], [4, 0, 0]]) def test_nan_policy_options(self): x = [1, 2, np.nan] y = [4, 5, 6] mt1 = stats.median_test(x, y, nan_policy='propagate') s, p, m, t = stats.median_test(x, y, nan_policy='omit') assert_equal(mt1, (np.nan, np.nan, np.nan, None)) assert_allclose(s, 0.31250000000000006) assert_allclose(p, 0.57615012203057869) assert_equal(m, 4.0) assert_equal(t, np.array([[0, 2],[2, 1]])) assert_raises(ValueError, stats.median_test, x, y, nan_policy='raise') def test_basic(self): # median_test calls chi2_contingency to compute the test statistic # and p-value. Make sure it hasn't screwed up the call... x = [1, 2, 3, 4, 5] y = [2, 4, 6, 8] stat, p, m, tbl = stats.median_test(x, y) assert_equal(m, 4) assert_equal(tbl, [[1, 2], [4, 2]]) exp_stat, exp_p, dof, e = stats.chi2_contingency(tbl) assert_allclose(stat, exp_stat) assert_allclose(p, exp_p) stat, p, m, tbl = stats.median_test(x, y, lambda_=0) assert_equal(m, 4) assert_equal(tbl, [[1, 2], [4, 2]]) exp_stat, exp_p, dof, e = stats.chi2_contingency(tbl, lambda_=0) assert_allclose(stat, exp_stat) assert_allclose(p, exp_p) stat, p, m, tbl = stats.median_test(x, y, correction=False) assert_equal(m, 4) assert_equal(tbl, [[1, 2], [4, 2]]) exp_stat, exp_p, dof, e = stats.chi2_contingency(tbl, correction=False) assert_allclose(stat, exp_stat) assert_allclose(p, exp_p)