def test_equivalence_equal(self):
# reference numbers from Jan and Shieh 2019, p. 5
means = self.means
nobs = self.nobs
stds = self.stds
n_groups = self.n_groups
eps = 0.5
res0 = anova_generic(means, stds**2, nobs, use_var="equal")
f = res0.statistic
res = equivalence_oneway_generic(f,
n_groups,
nobs.sum(),
eps,
res0.df,
alpha=0.05,
margin_type="wellek")
assert_allclose(res.pvalue, 0.0083, atol=0.001)
assert_equal(res.df, [3, 46])
# the agreement for f-stat looks too low
assert_allclose(f, 0.0926, atol=0.0006)
res = equivalence_oneway(self.data,
eps,
use_var="equal",
margin_type="wellek")
assert_allclose(res.pvalue, 0.0083, atol=0.001)
assert_equal(res.df, [3, 46])
def test_equivalence_welch(self):
# reference numbers from Jan and Shieh 2019, p. 6
means = self.means
nobs = self.nobs
stds = self.stds
n_groups = self.n_groups
vars_ = stds**2
eps = 0.5
res0 = anova_generic(means,
vars_,
nobs,
use_var="unequal",
welch_correction=False)
f_stat = res0.statistic
res = equivalence_oneway_generic(f_stat,
n_groups,
nobs.sum(),
eps,
res0.df,
alpha=0.05,
margin_type="wellek")
assert_allclose(res.pvalue, 0.0110, atol=0.001)
assert_allclose(res.df, [3.0, 22.6536], atol=0.0006)
# agreement for Welch f-stat looks too low b/c welch_correction=False
assert_allclose(f_stat, 0.1102, atol=0.007)
res = equivalence_oneway(self.data,
eps,
use_var="unequal",
margin_type="wellek")
assert_allclose(res.pvalue, 0.0110, atol=1e-4)
assert_allclose(res.df, [3.0, 22.6536], atol=0.0006)
assert_allclose(res.f_stat, 0.1102, atol=1e-4) # 0.007)
# check post-hoc power, JS p. 6
pow_ = _power_equivalence_oneway_emp(f_stat, n_groups, nobs, eps,
res0.df)
assert_allclose(pow_, 0.1552, atol=0.007)
pow_ = power_equivalence_oneway(eps,
eps,
nobs.sum(),
n_groups=n_groups,
df=None,
alpha=0.05,
margin_type="wellek")
assert_allclose(pow_, 0.05, atol=1e-13)
nobs_t = nobs.sum()
es = effectsize_oneway(means, vars_, nobs, use_var="unequal")
es = np.sqrt(es)
es_w0 = f2_to_wellek(es**2, n_groups)
es_w = np.sqrt(fstat_to_wellek(f_stat, n_groups, nobs_t / n_groups))
pow_ = power_equivalence_oneway(es_w,
eps,
nobs_t,
n_groups=n_groups,
df=None,
alpha=0.05,
margin_type="wellek")
assert_allclose(pow_, 0.1552, atol=0.007)
assert_allclose(es_w0, es_w, atol=0.007)
margin = wellek_to_f2(eps, n_groups)
pow_ = power_equivalence_oneway(es**2,
margin,
nobs_t,
n_groups=n_groups,
df=None,
alpha=0.05,
margin_type="f2")
assert_allclose(pow_, 0.1552, atol=0.007)