def setup_class(cls):
x = np.array([
77, 87, 88, 114, 151, 210, 219, 246, 253, 262, 296, 299, 306, 376,
428, 515, 666, 1310, 2611
])
cls.get_results() # attach k and results
cls.tm = TrimmedMean(x, cls.k / 19)
def test_vectorized(self, axis):
tm = self.tm
x = tm.data
x2 = np.column_stack((x, 2 * x))
if axis == 0:
tm2d = TrimmedMean(x2, self.k / 19, axis=0)
else:
tm2d = TrimmedMean(x2.T, self.k / 19, axis=1)
t1 = [tm.mean_trimmed, 2 * tm.mean_trimmed]
assert_allclose(tm2d.mean_trimmed, t1, rtol=1e-13)
t1 = [tm.var_winsorized, 4 * tm.var_winsorized]
assert_allclose(tm2d.var_winsorized, t1, rtol=1e-13)
t1 = [tm.std_mean_trimmed, 2 * tm.std_mean_trimmed]
assert_allclose(tm2d.std_mean_trimmed, t1, rtol=1e-13)
t1 = [tm.mean_winsorized, 2 * tm.mean_winsorized]
assert_allclose(tm2d.mean_winsorized, t1, rtol=1e-13)
t1 = [tm.std_mean_winsorized, 2 * tm.std_mean_winsorized]
assert_allclose(tm2d.std_mean_winsorized, t1, rtol=1e-13)
s2, pv2, df2 = tm2d.ttest_mean()
s, pv, df = tm.ttest_mean()
assert_allclose(s2, [s, s], rtol=1e-13)
assert_allclose(pv2, [pv, pv], rtol=1e-13)
assert_allclose(df2, df, rtol=1e-13)
s2, pv2, df2 = tm2d.ttest_mean(transform='winsorized')
s, pv, df = tm.ttest_mean(transform='winsorized')
assert_allclose(s2, [s, s], rtol=1e-13)
assert_allclose(pv2, [pv, pv], rtol=1e-13)
assert_allclose(df2, df, rtol=1e-13)
def anova_oneway(data, groups=None, use_var="unequal", welch_correction=True,
trim_frac=0):
"""oneway anova
This implements standard anova, Welch and Brown-Forsythe and trimmed
(Yuen) variants of them.
Parameters
----------
data : tuple of array_like or DataFrame or Series
Data for k independent samples, with k >= 2.
The data can be provided as a tuple or list of arrays or in long
format with outcome observations in ``data`` and group membershipt in
``groups``.
groups : ndarray or Series
If data is in long format, then groups is needed as indicator to which
group or sample and observations belongs.
use_var : {"unequal", "equal" or "bf"}
`use_var` specified how to treat heteroscedasticity, unequal variance,
across samples. Three approaches are available
"unequal" : Variances are not assumed to be equal across samples.
Heteroscedasticity is taken into account with Welch Anova and
Satterthwaite-Welch degrees of freedom.
This is the default.
"equal" : Variances are assumed to be equal across samples. This is
the standard Anova.
"bf: Variances are not assumed to be equal across samples. The method
is Browne-Forsythe (1971) for testing equality of means with the
corrected degrees of freedom by Merothra. The original BF degrees
of freedom are available as additional attributes in the results
instance, ``df_denom2`` and ``p_value2``.
trim_frac : float in [0, 0.5)
Optional trimming for Anova with trimmed mean and winsorized variances.
With the default trim_frac equal to zero, the oneway Anova statistics
are computed without trimming. If `trim_frac` is larger than zero,
then the largest and smallest observations in each sample are trimmed.
The number of trimmed observations is the fraction of number of
observations in the sample truncated to the next lower integer.
`trim_frac` has to be smaller than 0.5, however, if the fraction is
so large that there are not enough observations left over, then `nan`
will be returned.
Returns
-------
res : results instance
The returned HolderTuple instance has the following main attributes
and some additional information in other attributes.
statistic : float
Test statistic for k-sample mean comparison which is approximately
F-distributed.
pvalue : float
If f ``use_var="bf"``, then the p-value is based on corrected
degrees of freedom following Mehrotra 1997.
pvalue2 : float
This is the p-value based on degrees of freedom as in
Brown-Forsythe 1974 and is only available if ``use_var="bf"``.
df = (df_denom, df_num) : tuple of floats
Degreeds of freedom for the F-distribution depend on ``use_var``.
If f ``use_var="bf"``, then `df_denom` is for Mehrotra p-values
`df_denom2` is available for Brown-Forsythe 1974 p-values.
`df_num` is the same numerator degrees of freedom for both
p-values.
Notes
-----
Welch's anova is correctly sized (not liberal or conservative) in smaller
samples if the distribution of the samples is not very far away from the
normal distribution. The test can become liberal if the data is strongly
skewed. Welch's Anova can also be correctly sized for discrete
distributions with finite support, like Lickert scale data.
The trimmed version is robust to many non-normal distributions, it stays
correctly sized in many cases, and is more powerful in some cases with
skewness or heavy tails.
Trimming is currently based on the integer part of ``nobs * trim_frac``.
The default might change to including fractional observations as in the
original articles by Yuen.
See Also
--------
anova_generic
References
----------
Brown, Morton B., and Alan B. Forsythe. 1974. “The Small Sample Behavior
of Some Statistics Which Test the Equality of Several Means.”
Technometrics 16 (1) (February 1): 129–132. doi:10.2307/1267501.
Mehrotra, Devan V. 1997. “Improving the Brown-Forsythe Solution to the
Generalized Behrens-Fisher Problem.” Communications in Statistics -
Simulation and Computation 26 (3): 1139–1145.
doi:10.1080/03610919708813431.
"""
if groups is not None:
uniques = np.unique(groups)
data = [data[groups == uni] for uni in uniques]
else:
# uniques = None # not used yet, add to info?
pass
args = list(map(np.asarray, data))
if any([x.ndim != 1 for x in args]):
raise ValueError('data arrays have to be one-dimensional')
nobs = np.array([len(x) for x in args], float)
# n_groups = len(args) # not used
# means = np.array([np.mean(x, axis=0) for x in args], float)
# vars_ = np.array([np.var(x, ddof=1, axis=0) for x in args], float)
if trim_frac == 0:
means = np.array([x.mean() for x in args])
vars_ = np.array([x.var(ddof=1) for x in args])
else:
tms = [TrimmedMean(x, trim_frac) for x in args]
means = np.array([tm.mean_trimmed for tm in tms])
# R doesn't use uncorrected var_winsorized
# vars_ = np.array([tm.var_winsorized for tm in tms])
vars_ = np.array([tm.var_winsorized * (tm.nobs - 1) /
(tm.nobs_reduced - 1) for tm in tms])
# nobs_original = nobs # store just in case
nobs = np.array([tm.nobs_reduced for tm in tms])
res = anova_generic(means, vars_, nobs, use_var=use_var,
welch_correction=welch_correction)
return res