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)
def test_oneway_effectsize():
# examole 3 in Steiger 2004 Beyond the F-test, p. 169
F = 5
df1 = 3
df2 = 76
nobs = 80
ci = confint_noncentrality(F, (df1, df2),
alpha=0.05,
alternative="two-sided")
ci_es = confint_effectsize_oneway(F, (df1, df2), alpha=0.05)
ci_steiger = ci_es.ci_f * np.sqrt(4 / 3)
res_ci_steiger = [0.1764, 0.7367]
res_ci_nc = np.asarray([1.8666, 32.563])
assert_allclose(ci, res_ci_nc, atol=0.0001)
assert_allclose(ci_es.ci_f_corrected, res_ci_steiger, atol=0.00006)
assert_allclose(ci_steiger, res_ci_steiger, atol=0.00006)
assert_allclose(ci_es.ci_f**2, res_ci_nc / nobs, atol=0.00006)
assert_allclose(ci_es.ci_nc, res_ci_nc, atol=0.0001)