548 lines
22 KiB
Python
548 lines
22 KiB
Python
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"""
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Created on Wed Mar 18 17:45:51 2020
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Author: Josef Perktold
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License: BSD-3
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"""
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import numpy as np
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from numpy.testing import assert_allclose, assert_equal
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import pytest
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from statsmodels.regression.linear_model import OLS
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import statsmodels.stats.power as smpwr
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import statsmodels.stats.oneway as smo # needed for function with `test`
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from statsmodels.stats.oneway import (
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confint_effectsize_oneway, confint_noncentrality, effectsize_oneway,
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anova_oneway,
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anova_generic, equivalence_oneway, equivalence_oneway_generic,
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power_equivalence_oneway, _power_equivalence_oneway_emp,
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f2_to_wellek, fstat_to_wellek, wellek_to_f2)
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from statsmodels.stats.robust_compare import scale_transform
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from statsmodels.stats.contrast import (
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wald_test_noncent_generic, wald_test_noncent, _offset_constraint)
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def test_oneway_effectsize():
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# examole 3 in Steiger 2004 Beyond the F-test, p. 169
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F = 5
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df1 = 3
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df2 = 76
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nobs = 80
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ci = confint_noncentrality(F, (df1, df2), alpha=0.05,
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alternative="two-sided")
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ci_es = confint_effectsize_oneway(F, (df1, df2), alpha=0.05)
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ci_steiger = ci_es.ci_f * np.sqrt(4 / 3)
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res_ci_steiger = [0.1764, 0.7367]
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res_ci_nc = np.asarray([1.8666, 32.563])
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assert_allclose(ci, res_ci_nc, atol=0.0001)
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assert_allclose(ci_es.ci_f_corrected, res_ci_steiger, atol=0.00006)
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assert_allclose(ci_steiger, res_ci_steiger, atol=0.00006)
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assert_allclose(ci_es.ci_f**2, res_ci_nc / nobs, atol=0.00006)
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assert_allclose(ci_es.ci_nc, res_ci_nc, atol=0.0001)
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def test_effectsize_power():
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# example and results from PASS documentation
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n_groups = 3
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means = [527.86, 660.43, 649.14]
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vars_ = 107.4304**2
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nobs = 12
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es = effectsize_oneway(means, vars_, nobs, use_var="equal", ddof_between=0)
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es = np.sqrt(es)
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alpha = 0.05
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power = 0.8
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nobs_t = nobs * n_groups
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kwds = {'effect_size': es, 'nobs': nobs_t, 'alpha': alpha, 'power': power,
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'k_groups': n_groups}
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from statsmodels.stats.power import FTestAnovaPower
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res_pow = 0.8251
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res_es = 0.559
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kwds_ = kwds.copy()
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del kwds_['power']
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p = FTestAnovaPower().power(**kwds_)
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assert_allclose(p, res_pow, atol=0.0001)
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assert_allclose(es, res_es, atol=0.0006)
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# example unequal sample sizes
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nobs = np.array([15, 9, 9])
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kwds['nobs'] = nobs
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es = effectsize_oneway(means, vars_, nobs, use_var="equal", ddof_between=0)
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es = np.sqrt(es)
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kwds['effect_size'] = es
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p = FTestAnovaPower().power(**kwds_)
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res_pow = 0.8297
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res_es = 0.590
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assert_allclose(p, res_pow, atol=0.005) # lower than print precision
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assert_allclose(es, res_es, atol=0.0006)
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def test_effectsize_fstat():
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# results from R package `effectsize`, confint is 0.9 confidence
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# > es = F_to_eta2(45.8, 3, 35)
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Eta_Sq_partial = 0.796983758700696
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CI_eta2 = 0.685670133284926, 0.855981325777856 # reformated from output
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# > es = F_to_epsilon2(45.8, 3, 35)
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Epsilon_Sq_partial = 0.779582366589327
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CI_eps2 = 0.658727573280777, 0.843636867987386
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# > es = F_to_omega2(45.8, 3, 35)
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Omega_Sq_partial = 0.775086505190311
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CI_omega2 = 0.65286429480169, 0.840179680453464
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# > es = F_to_f(45.8, 3, 35)
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Cohens_f_partial = 1.98134153686695
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CI_f = 1.47694659580859, 2.43793847155554
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f_stat, df1, df2 = 45.8, 3, 35
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# nobs = df1 + df2 + 1 # not directly used in the following, only df
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fes = smo._fstat2effectsize(f_stat, (df1, df2))
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assert_allclose(np.sqrt(fes.f2), Cohens_f_partial, rtol=1e-13)
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assert_allclose(fes.eta2, Eta_Sq_partial, rtol=1e-13)
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assert_allclose(fes.eps2, Epsilon_Sq_partial, rtol=1e-13)
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assert_allclose(fes.omega2, Omega_Sq_partial, rtol=1e-13)
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ci_nc = confint_noncentrality(f_stat, (df1, df2), alpha=0.1)
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# the following replicates R package effectsize
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ci_es = smo._fstat2effectsize(ci_nc / df1, (df1, df2))
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assert_allclose(ci_es.eta2, CI_eta2, rtol=2e-4)
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assert_allclose(ci_es.eps2, CI_eps2, rtol=2e-4)
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assert_allclose(ci_es.omega2, CI_omega2, rtol=2e-4)
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assert_allclose(np.sqrt(ci_es.f2), CI_f, rtol=2e-4)
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def test_effectsize_fstat_stata():
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# reference numbers computed with Stata 14
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# Stata 16 does not seem to have confint for omega2
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# esizei 2 40 7.47403193349075, level(90)
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eta2 = 0.2720398648288652
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lb_eta2 = 0.0742092468714613
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ub_eta2 = 0.4156116886974804
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omega2 = 0.2356418580703085
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lb_omega2 = 0.0279197092150344
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ub_omega2 = 0.3863922731323545
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# level = 90
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f_stat, df1, df2 = 7.47403193349075, 2, 40
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fes = smo._fstat2effectsize(f_stat, (df1, df2))
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assert_allclose(fes.eta2, eta2, rtol=1e-13)
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assert_allclose(fes.omega2, omega2, rtol=0.02) # low agreement
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ci_es = smo.confint_effectsize_oneway(f_stat, (df1, df2), alpha=0.1)
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assert_allclose(ci_es.eta2, (lb_eta2, ub_eta2), rtol=1e-4)
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assert_allclose(ci_es.ci_omega2, (lb_omega2, ub_omega2), rtol=0.025)
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@pytest.mark.parametrize("center", ['median', 'mean', 'trimmed'])
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def test_scale_transform(center):
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x = np.random.randn(5, 3)
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xt = scale_transform(x, center=center, transform='abs', trim_frac=0.2,
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axis=0)
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xtt = scale_transform(x.T, center=center, transform='abs', trim_frac=0.2,
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axis=1)
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assert_allclose(xt.T, xtt, rtol=1e-13)
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xt0 = scale_transform(x[:, 0], center=center, transform='abs',
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trim_frac=0.2)
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assert_allclose(xt0, xt[:, 0], rtol=1e-13)
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assert_allclose(xt0, xtt[0, :], rtol=1e-13)
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class TestOnewayEquivalenc:
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@classmethod
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def setup_class(cls):
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y0 = [112.488, 103.738, 86.344, 101.708, 95.108, 105.931,
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95.815, 91.864, 102.479, 102.644]
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y1 = [100.421, 101.966, 99.636, 105.983, 88.377, 102.618,
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105.486, 98.662, 94.137, 98.626, 89.367, 106.204]
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y2 = [84.846, 100.488, 119.763, 103.736, 93.141, 108.254,
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99.510, 89.005, 108.200, 82.209, 100.104, 103.706,
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107.067]
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y3 = [100.825, 100.255, 103.363, 93.230, 95.325, 100.288,
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94.750, 107.129, 98.246, 96.365, 99.740, 106.049,
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92.691, 93.111, 98.243]
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n_groups = 4
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arrs_w = [np.asarray(yi) for yi in [y0, y1, y2, y3]]
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nobs = np.asarray([len(yi) for yi in arrs_w])
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nobs_mean = np.mean(nobs)
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means = np.asarray([yi.mean() for yi in arrs_w])
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stds = np.asarray([yi.std(ddof=1) for yi in arrs_w])
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cls.data = arrs_w # TODO use `data`
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cls.means = means
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cls.nobs = nobs
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cls.stds = stds
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cls.n_groups = n_groups
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cls.nobs_mean = nobs_mean
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def test_equivalence_equal(self):
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# reference numbers from Jan and Shieh 2019, p. 5
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means = self.means
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nobs = self.nobs
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stds = self.stds
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n_groups = self.n_groups
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eps = 0.5
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res0 = anova_generic(means, stds**2, nobs, use_var="equal")
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f = res0.statistic
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res = equivalence_oneway_generic(f, n_groups, nobs.sum(), eps,
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res0.df, alpha=0.05,
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margin_type="wellek")
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assert_allclose(res.pvalue, 0.0083, atol=0.001)
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assert_equal(res.df, [3, 46])
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# the agreement for f-stat looks too low
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assert_allclose(f, 0.0926, atol=0.0006)
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res = equivalence_oneway(self.data, eps, use_var="equal",
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margin_type="wellek")
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assert_allclose(res.pvalue, 0.0083, atol=0.001)
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assert_equal(res.df, [3, 46])
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def test_equivalence_welch(self):
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# reference numbers from Jan and Shieh 2019, p. 6
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means = self.means
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nobs = self.nobs
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stds = self.stds
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n_groups = self.n_groups
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vars_ = stds**2
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eps = 0.5
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res0 = anova_generic(means, vars_, nobs, use_var="unequal",
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welch_correction=False)
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f_stat = res0.statistic
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res = equivalence_oneway_generic(f_stat, n_groups, nobs.sum(), eps,
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res0.df, alpha=0.05,
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margin_type="wellek")
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assert_allclose(res.pvalue, 0.0110, atol=0.001)
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assert_allclose(res.df, [3.0, 22.6536], atol=0.0006)
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# agreement for Welch f-stat looks too low b/c welch_correction=False
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assert_allclose(f_stat, 0.1102, atol=0.007)
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res = equivalence_oneway(self.data, eps, use_var="unequal",
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margin_type="wellek")
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assert_allclose(res.pvalue, 0.0110, atol=1e-4)
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assert_allclose(res.df, [3.0, 22.6536], atol=0.0006)
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assert_allclose(res.f_stat, 0.1102, atol=1e-4) # 0.007)
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# check post-hoc power, JS p. 6
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pow_ = _power_equivalence_oneway_emp(f_stat, n_groups, nobs, eps,
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res0.df)
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assert_allclose(pow_, 0.1552, atol=0.007)
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pow_ = power_equivalence_oneway(eps, eps, nobs.sum(),
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n_groups=n_groups, df=None, alpha=0.05,
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margin_type="wellek")
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assert_allclose(pow_, 0.05, atol=1e-13)
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nobs_t = nobs.sum()
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es = effectsize_oneway(means, vars_, nobs, use_var="unequal")
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es = np.sqrt(es)
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es_w0 = f2_to_wellek(es**2, n_groups)
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es_w = np.sqrt(fstat_to_wellek(f_stat, n_groups, nobs_t / n_groups))
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pow_ = power_equivalence_oneway(es_w, eps, nobs_t,
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n_groups=n_groups, df=None, alpha=0.05,
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margin_type="wellek")
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assert_allclose(pow_, 0.1552, atol=0.007)
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assert_allclose(es_w0, es_w, atol=0.007)
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margin = wellek_to_f2(eps, n_groups)
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pow_ = power_equivalence_oneway(es**2, margin, nobs_t,
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n_groups=n_groups, df=None, alpha=0.05,
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margin_type="f2")
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assert_allclose(pow_, 0.1552, atol=0.007)
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class TestOnewayScale:
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@classmethod
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def setup_class(cls):
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yt0 = np.array([102., 320., 0., 107., 198., 200., 4., 20., 110., 128.,
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7., 119., 309.])
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yt1 = np.array([0., 1., 228., 81., 87., 119., 79., 181., 43., 12., 90.,
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105., 108., 119., 0., 9.])
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yt2 = np.array([33., 294., 134., 216., 83., 105., 69., 20., 20., 63.,
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98., 155., 78., 75.])
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y0 = np.array([452., 874., 554., 447., 356., 754., 558., 574., 664.,
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682., 547., 435., 245.])
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y1 = np.array([546., 547., 774., 465., 459., 665., 467., 365., 589.,
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534., 456., 651., 654., 665., 546., 537.])
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y2 = np.array([785., 458., 886., 536., 669., 857., 821., 772., 732.,
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689., 654., 597., 830., 827.])
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n_groups = 3
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data = [y0, y1, y2]
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nobs = np.asarray([len(yi) for yi in data])
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nobs_mean = np.mean(nobs)
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means = np.asarray([yi.mean() for yi in data])
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stds = np.asarray([yi.std(ddof=1) for yi in data])
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cls.data = data
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cls.data_transformed = [yt0, yt1, yt2]
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cls.means = means
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cls.nobs = nobs
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cls.stds = stds
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cls.n_groups = n_groups
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cls.nobs_mean = nobs_mean
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def test_means(self):
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# library onewaystats, BF test for equality of means
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# st = bf.test(y ~ g, df3)
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statistic = 7.10900606421182
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parameter = [2, 31.4207256105052]
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p_value = 0.00283841965791224
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# method = 'Brown-Forsythe Test'
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res = anova_oneway(self.data, use_var="bf")
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# R bf.test uses original BF df_num
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assert_allclose(res.pvalue2, p_value, rtol=1e-13)
|
||
|
|
assert_allclose(res.statistic, statistic, rtol=1e-13)
|
||
|
|
assert_allclose([res.df_num2, res.df_denom], parameter)
|
||
|
|
|
||
|
|
def test_levene(self):
|
||
|
|
data = self.data
|
||
|
|
|
||
|
|
# lawstat: Test Statistic = 1.0866123063642, p-value = 0.3471072204516
|
||
|
|
statistic = 1.0866123063642
|
||
|
|
p_value = 0.3471072204516
|
||
|
|
res0 = smo.test_scale_oneway(data, method='equal', center='median',
|
||
|
|
transform='abs', trim_frac_mean=0.2)
|
||
|
|
assert_allclose(res0.pvalue, p_value, rtol=1e-13)
|
||
|
|
assert_allclose(res0.statistic, statistic, rtol=1e-13)
|
||
|
|
|
||
|
|
# library car
|
||
|
|
# > lt = leveneTest(y ~ g, df3, center=mean, trim=0.2)
|
||
|
|
statistic = 1.10732113109744
|
||
|
|
p_value = 0.340359251994645
|
||
|
|
df = [2, 40]
|
||
|
|
res0 = smo.test_scale_oneway(data, method='equal', center='trimmed',
|
||
|
|
transform='abs', trim_frac_mean=0.2)
|
||
|
|
assert_allclose(res0.pvalue, p_value, rtol=1e-13)
|
||
|
|
assert_allclose(res0.statistic, statistic, rtol=1e-13)
|
||
|
|
assert_allclose(res0.df, df)
|
||
|
|
|
||
|
|
# library(onewaytests)
|
||
|
|
# test uses mean as center
|
||
|
|
# > st = homog.test(y ~ g, df3)
|
||
|
|
statistic = 1.07894485177512
|
||
|
|
parameter = [2, 40] # df
|
||
|
|
p_value = 0.349641166869223
|
||
|
|
# method = "Levene's Homogeneity Test"
|
||
|
|
res0 = smo.test_scale_oneway(data, method='equal', center='mean',
|
||
|
|
transform='abs', trim_frac_mean=0.2)
|
||
|
|
assert_allclose(res0.pvalue, p_value, rtol=1e-13)
|
||
|
|
assert_allclose(res0.statistic, statistic, rtol=1e-13)
|
||
|
|
assert_allclose(res0.df, parameter)
|
||
|
|
|
||
|
|
# > st = homog.test(y ~ g, df3, method = "Bartlett")
|
||
|
|
statistic = 3.01982414477323
|
||
|
|
# parameter = 2 # scipy bartlett does not return df
|
||
|
|
p_value = 0.220929402900495
|
||
|
|
# method = "Bartlett's Homogeneity Test"
|
||
|
|
# Bartlett is in scipy.stats
|
||
|
|
from scipy import stats
|
||
|
|
stat, pv = stats.bartlett(*data)
|
||
|
|
assert_allclose(pv, p_value, rtol=1e-13)
|
||
|
|
assert_allclose(stat, statistic, rtol=1e-13)
|
||
|
|
|
||
|
|
def test_options(self):
|
||
|
|
# regression tests for options,
|
||
|
|
# many might not be implemented in other packages
|
||
|
|
data = self.data
|
||
|
|
|
||
|
|
# regression numbers from initial run
|
||
|
|
statistic, p_value = 1.0173464626246675, 0.3763806150460239
|
||
|
|
df = (2.0, 24.40374758005409)
|
||
|
|
res = smo.test_scale_oneway(data, method='unequal', center='median',
|
||
|
|
transform='abs', trim_frac_mean=0.2)
|
||
|
|
assert_allclose(res.pvalue, p_value, rtol=1e-13)
|
||
|
|
assert_allclose(res.statistic, statistic, rtol=1e-13)
|
||
|
|
assert_allclose(res.df, df)
|
||
|
|
|
||
|
|
statistic, p_value = 1.0329722145270606, 0.3622778213868562
|
||
|
|
df = (1.83153791573948, 30.6733640949525)
|
||
|
|
p_value2 = 0.3679999679787619
|
||
|
|
df2 = (2, 30.6733640949525)
|
||
|
|
res = smo.test_scale_oneway(data, method='bf', center='median',
|
||
|
|
transform='abs', trim_frac_mean=0.2)
|
||
|
|
assert_allclose(res.pvalue, p_value, rtol=1e-13)
|
||
|
|
assert_allclose(res.statistic, statistic, rtol=1e-13)
|
||
|
|
assert_allclose(res.df, df)
|
||
|
|
assert_allclose(res.pvalue2, p_value2, rtol=1e-13)
|
||
|
|
assert_allclose(res.df2, df2)
|
||
|
|
|
||
|
|
statistic, p_value = 1.7252431333701745, 0.19112038168209514
|
||
|
|
df = (2.0, 40.0)
|
||
|
|
res = smo.test_scale_oneway(data, method='equal', center='mean',
|
||
|
|
transform='square', trim_frac_mean=0.2)
|
||
|
|
assert_allclose(res.pvalue, p_value, rtol=1e-13)
|
||
|
|
assert_allclose(res.statistic, statistic, rtol=1e-13)
|
||
|
|
assert_equal(res.df, df)
|
||
|
|
|
||
|
|
statistic, p_value = 0.4129696057329463, 0.6644711582864451
|
||
|
|
df = (2.0, 40.0)
|
||
|
|
res = smo.test_scale_oneway(data, method='equal', center='mean',
|
||
|
|
transform=lambda x: np.log(x * x), # noqa
|
||
|
|
trim_frac_mean=0.2)
|
||
|
|
assert_allclose(res.pvalue, p_value, rtol=1e-13)
|
||
|
|
assert_allclose(res.statistic, statistic, rtol=1e-13)
|
||
|
|
assert_allclose(res.df, df)
|
||
|
|
|
||
|
|
# compare no transform with standard anova
|
||
|
|
res = smo.test_scale_oneway(data, method='unequal', center=0,
|
||
|
|
transform='identity', trim_frac_mean=0.2)
|
||
|
|
res2 = anova_oneway(self.data, use_var="unequal")
|
||
|
|
|
||
|
|
assert_allclose(res.pvalue, res2.pvalue, rtol=1e-13)
|
||
|
|
assert_allclose(res.statistic, res2.statistic, rtol=1e-13)
|
||
|
|
assert_allclose(res.df, res2.df)
|
||
|
|
|
||
|
|
def test_equivalence(self):
|
||
|
|
data = self.data
|
||
|
|
|
||
|
|
# compare no transform with standard anova
|
||
|
|
res = smo.equivalence_scale_oneway(data, 0.5, method='unequal',
|
||
|
|
center=0,
|
||
|
|
transform='identity')
|
||
|
|
res2 = equivalence_oneway(self.data, 0.5, use_var="unequal")
|
||
|
|
|
||
|
|
assert_allclose(res.pvalue, res2.pvalue, rtol=1e-13)
|
||
|
|
assert_allclose(res.statistic, res2.statistic, rtol=1e-13)
|
||
|
|
assert_allclose(res.df, res2.df)
|
||
|
|
|
||
|
|
res = smo.equivalence_scale_oneway(data, 0.5, method='bf',
|
||
|
|
center=0,
|
||
|
|
transform='identity')
|
||
|
|
res2 = equivalence_oneway(self.data, 0.5, use_var="bf")
|
||
|
|
|
||
|
|
assert_allclose(res.pvalue, res2.pvalue, rtol=1e-13)
|
||
|
|
assert_allclose(res.statistic, res2.statistic, rtol=1e-13)
|
||
|
|
assert_allclose(res.df, res2.df)
|
||
|
|
|
||
|
|
|
||
|
|
class TestOnewayOLS:
|
||
|
|
|
||
|
|
@classmethod
|
||
|
|
def setup_class(cls):
|
||
|
|
y0 = [112.488, 103.738, 86.344, 101.708, 95.108, 105.931,
|
||
|
|
95.815, 91.864, 102.479, 102.644]
|
||
|
|
y1 = [100.421, 101.966, 99.636, 105.983, 88.377, 102.618,
|
||
|
|
105.486, 98.662, 94.137, 98.626, 89.367, 106.204]
|
||
|
|
y2 = [84.846, 100.488, 119.763, 103.736, 93.141, 108.254,
|
||
|
|
99.510, 89.005, 108.200, 82.209, 100.104, 103.706,
|
||
|
|
107.067]
|
||
|
|
y3 = [100.825, 100.255, 103.363, 93.230, 95.325, 100.288,
|
||
|
|
94.750, 107.129, 98.246, 96.365, 99.740, 106.049,
|
||
|
|
92.691, 93.111, 98.243]
|
||
|
|
|
||
|
|
cls.k_groups = k = 4
|
||
|
|
cls.data = data = [y0, y1, y2, y3]
|
||
|
|
cls.nobs = nobs = np.asarray([len(yi) for yi in data])
|
||
|
|
groups = np.repeat(np.arange(k), nobs)
|
||
|
|
cls.ex = (groups[:, None] == np.arange(k)).astype(np.int64)
|
||
|
|
cls.y = np.concatenate(data)
|
||
|
|
|
||
|
|
def test_ols_noncentrality(self):
|
||
|
|
k = self.k_groups
|
||
|
|
|
||
|
|
res_ols = OLS(self.y, self.ex).fit()
|
||
|
|
nobs_t = res_ols.model.nobs
|
||
|
|
|
||
|
|
# constraint
|
||
|
|
c_equal = -np.eye(k)[1:]
|
||
|
|
c_equal[:, 0] = 1
|
||
|
|
v = np.zeros(c_equal.shape[0])
|
||
|
|
|
||
|
|
# noncentrality at estimated parameters
|
||
|
|
wt = res_ols.wald_test(c_equal, scalar=True)
|
||
|
|
df_num, df_denom = wt.df_num, wt.df_denom
|
||
|
|
|
||
|
|
cov_p = res_ols.cov_params()
|
||
|
|
|
||
|
|
nc_wt = wald_test_noncent_generic(res_ols.params, c_equal, v, cov_p,
|
||
|
|
diff=None, joint=True)
|
||
|
|
assert_allclose(nc_wt, wt.statistic * wt.df_num, rtol=1e-13)
|
||
|
|
|
||
|
|
nc_wt2 = wald_test_noncent(res_ols.params, c_equal, v, res_ols,
|
||
|
|
diff=None, joint=True)
|
||
|
|
assert_allclose(nc_wt2, nc_wt, rtol=1e-13)
|
||
|
|
|
||
|
|
es_ols = nc_wt / nobs_t
|
||
|
|
es_oneway = smo.effectsize_oneway(res_ols.params, res_ols.scale,
|
||
|
|
self.nobs, use_var="equal")
|
||
|
|
assert_allclose(es_ols, es_oneway, rtol=1e-13)
|
||
|
|
|
||
|
|
alpha = 0.05
|
||
|
|
pow_ols = smpwr.ftest_power(np.sqrt(es_ols), df_denom, df_num, alpha,
|
||
|
|
ncc=1)
|
||
|
|
pow_oneway = smpwr.ftest_anova_power(np.sqrt(es_oneway), nobs_t, alpha,
|
||
|
|
k_groups=k, df=None)
|
||
|
|
assert_allclose(pow_ols, pow_oneway, rtol=1e-13)
|
||
|
|
|
||
|
|
# noncentrality at other params
|
||
|
|
params_alt = res_ols.params * 0.75
|
||
|
|
# compute constraint value so we can get noncentrality from wald_test
|
||
|
|
v_off = _offset_constraint(c_equal, res_ols.params, params_alt)
|
||
|
|
wt_off = res_ols.wald_test((c_equal, v + v_off), scalar=True)
|
||
|
|
nc_wt_off = wald_test_noncent_generic(params_alt, c_equal, v,
|
||
|
|
cov_p, diff=None, joint=True)
|
||
|
|
assert_allclose(nc_wt_off, wt_off.statistic * wt_off.df_num,
|
||
|
|
rtol=1e-13)
|
||
|
|
|
||
|
|
# check vectorized version, joint=False
|
||
|
|
nc_wt_vec = wald_test_noncent_generic(params_alt, c_equal, v,
|
||
|
|
cov_p, diff=None, joint=False)
|
||
|
|
for i in range(c_equal.shape[0]):
|
||
|
|
nc_wt_i = wald_test_noncent_generic(params_alt, c_equal[i : i + 1], # noqa
|
||
|
|
v[i : i + 1], cov_p, diff=None, # noqa
|
||
|
|
joint=False)
|
||
|
|
assert_allclose(nc_wt_vec[i], nc_wt_i, rtol=1e-13)
|
||
|
|
|
||
|
|
|
||
|
|
def test_simulate_equivalence():
|
||
|
|
# regression test, needs large k_mc to be reliable
|
||
|
|
|
||
|
|
k_groups = 4
|
||
|
|
k_repl = 10
|
||
|
|
nobs = np.array([10, 12, 13, 15]) * k_repl
|
||
|
|
means = np.array([-1, 0, 0, 1]) * 0.12
|
||
|
|
vars_ = np.array([1, 2, 3, 4])
|
||
|
|
nobs_t = nobs.sum()
|
||
|
|
|
||
|
|
eps = 0.0191 * 10
|
||
|
|
opt_var = ["unequal", "equal", "bf"]
|
||
|
|
k_mc = 100
|
||
|
|
np.random.seed(987126)
|
||
|
|
res_mc = smo.simulate_power_equivalence_oneway(
|
||
|
|
means, nobs, eps, vars_=vars_, k_mc=k_mc, trim_frac=0.1,
|
||
|
|
options_var=opt_var, margin_type="wellek")
|
||
|
|
|
||
|
|
frac_reject = (res_mc.pvalue <= 0.05).sum(0) / k_mc
|
||
|
|
assert_allclose(frac_reject, [0.17, 0.18, 0.14], atol=0.001)
|
||
|
|
# result with k_mc = 10000 is [0.1466, 0.1871, 0.1606]
|
||
|
|
# similar to asy below, but not very close for all
|
||
|
|
|
||
|
|
es_alt_li = []
|
||
|
|
for uv in opt_var:
|
||
|
|
es = effectsize_oneway(means, vars_, nobs, use_var=uv)
|
||
|
|
es_alt_li.append(es)
|
||
|
|
|
||
|
|
# compute asy power as comparison
|
||
|
|
margin = wellek_to_f2(eps, k_groups)
|
||
|
|
pow_ = [power_equivalence_oneway(
|
||
|
|
es_, margin, nobs_t, n_groups=k_groups, df=None, alpha=0.05,
|
||
|
|
margin_type="f2") for es_ in es_alt_li]
|
||
|
|
# regression test numbers
|
||
|
|
assert_allclose(pow_, [0.147749, 0.173358, 0.177412], atol=0.007)
|