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_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)