def test_effectsize_fstat():
# results from R package `effectsize`, confint is 0.9 confidence
# > es = F_to_eta2(45.8, 3, 35)
Eta_Sq_partial = 0.796983758700696
CI_eta2 = 0.685670133284926, 0.855981325777856 # reformated from output
# > es = F_to_epsilon2(45.8, 3, 35)
Epsilon_Sq_partial = 0.779582366589327
CI_eps2 = 0.658727573280777, 0.843636867987386
# > es = F_to_omega2(45.8, 3, 35)
Omega_Sq_partial = 0.775086505190311
CI_omega2 = 0.65286429480169, 0.840179680453464
# > es = F_to_f(45.8, 3, 35)
Cohens_f_partial = 1.98134153686695
CI_f = 1.47694659580859, 2.43793847155554
f_stat, df1, df2 = 45.8, 3, 35
# nobs = df1 + df2 + 1 # not directly used in the following, only df
fes = smo._fstat2effectsize(f_stat, (df1, df2))
assert_allclose(np.sqrt(fes.f2), Cohens_f_partial, rtol=1e-13)
assert_allclose(fes.eta2, Eta_Sq_partial, rtol=1e-13)
assert_allclose(fes.eps2, Epsilon_Sq_partial, rtol=1e-13)
assert_allclose(fes.omega2, Omega_Sq_partial, rtol=1e-13)
ci_nc = confint_noncentrality(f_stat, (df1, df2), alpha=0.1)
# the following replicates R package effectsize
ci_es = smo._fstat2effectsize(ci_nc / df1, (df1, df2))
assert_allclose(ci_es.eta2, CI_eta2, rtol=2e-4)
assert_allclose(ci_es.eps2, CI_eps2, rtol=2e-4)
assert_allclose(ci_es.omega2, CI_omega2, rtol=2e-4)
assert_allclose(np.sqrt(ci_es.f2), CI_f, rtol=2e-4)
def test_effectsize_fstat_stata():
# reference numbers computed with Stata 14
# Stata 16 does not seem to have confint for omega2
# esizei 2 40 7.47403193349075, level(90)
eta2 = 0.2720398648288652
lb_eta2 = 0.0742092468714613
ub_eta2 = 0.4156116886974804
omega2 = 0.2356418580703085
lb_omega2 = 0.0279197092150344
ub_omega2 = 0.3863922731323545
# level = 90
f_stat, df1, df2 = 7.47403193349075, 2, 40
fes = smo._fstat2effectsize(f_stat, (df1, df2))
assert_allclose(fes.eta2, eta2, rtol=1e-13)
assert_allclose(fes.omega2, omega2, rtol=0.02) # low agreement
ci_es = smo.confint_effectsize_oneway(f_stat, (df1, df2), alpha=0.1)
assert_allclose(ci_es.eta2, (lb_eta2, ub_eta2), rtol=1e-4)
assert_allclose(ci_es.ci_omega2, (lb_omega2, ub_omega2), rtol=0.025)