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)
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)