def test_scale_oneway(data, method='bfm', center='median', transform='abs',
trim_frac_mean=0.1, trim_frac_anova=0.):
"""Oneway Anova test for equal scale, variance or dispersion
This hypothesis test performs a oneway anova test on transformed data and
includes Levene or Brown-Forsythe tests for equal variances as special
cases.
Parameters
----------
data
method "equal", "unequal", "bfm"
center : "median", "mean", "trimmed" or float
transform : "abs", "square" or callable
trim_frac_mean=0.1,
trim_frac_anova=0.
Returns
-------
HoderTuple instance
See Also
--------
anova_oneway
scale_transform
"""
data = map(np.asarray, data)
xxd = [scale_transform(x, center=center, transform=transform,
trim_frac=trim_frac_mean) for x in data]
res = anova_oneway(xxd, groups=None, use_var=method,
welch_correction=True, trim_frac=trim_frac_anova)
res.data_transformed = xxd
return res
def equivalence_scale_oneway(data,
equiv_margin,
method='bfm',
center='median',
transform='abs',
trim_frac_mean=0.,
trim_frac_anova=0.):
"""Oneway Anova test for equivalence of scale, variance or dispersion
This hypothesis test performs a oneway equivalence anova test on
transformed data.
Note, the interpretation of the equivalence margin `equiv_margin` will
depend on the transformation of the data. Transformations like
absolute deviation are not scaled to correspond to the variance under
normal distribution.
"""
data = map(np.asarray, data)
xxd = [
scale_transform(x,
center=center,
transform=transform,
trim_frac=trim_frac_mean) for x in data
]
res = equivalence_oneway(xxd,
equiv_margin,
use_var=method,
welch_correction=True,
trim_frac=trim_frac_anova)
res.x_transformed = xxd
return res
def test_scale_transform(center):
x = np.random.randn(5, 3)
xt = scale_transform(x,
center=center,
transform='abs',
trim_frac=0.2,
axis=0)
xtt = scale_transform(x.T,
center=center,
transform='abs',
trim_frac=0.2,
axis=1)
assert_allclose(xt.T, xtt, rtol=1e-13)
xt0 = scale_transform(x[:, 0],
center=center,
transform='abs',
trim_frac=0.2)
assert_allclose(xt0, xt[:, 0], rtol=1e-13)
assert_allclose(xt0, xtt[0, :], rtol=1e-13)
def test_scale_oneway(data, method="bf", center="median", transform="abs",
trim_frac_mean=0.1, trim_frac_anova=0.0):
"""Oneway Anova test for equal scale, variance or dispersion
This hypothesis test performs a oneway anova test on transformed data and
includes Levene and Brown-Forsythe tests for equal variances as special
cases.
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 membership in ``groups``.
method : {"unequal", "equal" or "bf"}
How to treat heteroscedasticity across samples. This is used as
`use_var` option in `anova_oneway` and refers to the variance of the
transformed data, i.e. assumption is on 4th moment if squares are used
as transform.
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``.
center : "median", "mean", "trimmed" or float
Statistic used for centering observations. If a float, then this
value is used to center. Default is median.
transform : "abs", "square" or callable
Transformation for the centered observations. If a callable, then this
function is called on the centered data.
Default is absolute value.
trim_frac_mean=0.1 : float in [0, 0.5)
Trim fraction for the trimmed mean when `center` is "trimmed"
trim_frac_anova : 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.
see ``trim_frac`` option in `anova_oneway`
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 ``method="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 ``method="bf"``.
df : (df_denom, df_num)
Tuple containing degrees of freedom for the F-distribution depend
on ``method``. If ``method="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.
See Also
--------
anova_oneway
scale_transform
"""
data = map(np.asarray, data)
xxd = [scale_transform(x, center=center, transform=transform,
trim_frac=trim_frac_mean) for x in data]
res = anova_oneway(xxd, groups=None, use_var=method,
welch_correction=True, trim_frac=trim_frac_anova)
res.data_transformed = xxd
return res
def equivalence_scale_oneway(data, equiv_margin, method='bf', center='median',
transform='abs', trim_frac_mean=0.,
trim_frac_anova=0.):
"""Oneway Anova test for equivalence of scale, variance or dispersion
This hypothesis test performs a oneway equivalence anova test on
transformed data.
Note, the interpretation of the equivalence margin `equiv_margin` will
depend on the transformation of the data. Transformations like
absolute deviation are not scaled to correspond to the variance under
normal distribution.
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 membership in ``groups``.
equiv_margin : float
Equivalence margin in terms of effect size. Effect size can be chosen
with `margin_type`. default is squared Cohen's f.
method : {"unequal", "equal" or "bf"}
How to treat heteroscedasticity across samples. This is used as
`use_var` option in `anova_oneway` and refers to the variance of the
transformed data, i.e. assumption is on 4th moment if squares are used
as transform.
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``.
center : "median", "mean", "trimmed" or float
Statistic used for centering observations. If a float, then this
value is used to center. Default is median.
transform : "abs", "square" or callable
Transformation for the centered observations. If a callable, then this
function is called on the centered data.
Default is absolute value.
trim_frac_mean : float in [0, 0.5)
Trim fraction for the trimmed mean when `center` is "trimmed"
trim_frac_anova : 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.
see ``trim_frac`` option in `anova_oneway`
Returns
-------
results : instance of HolderTuple class
The two main attributes are test statistic `statistic` and p-value
`pvalue`.
See Also
--------
anova_oneway
scale_transform
equivalence_oneway
"""
data = map(np.asarray, data)
xxd = [scale_transform(x, center=center, transform=transform,
trim_frac=trim_frac_mean) for x in data]
res = equivalence_oneway(xxd, equiv_margin, use_var=method,
welch_correction=True, trim_frac=trim_frac_anova)
res.x_transformed = xxd
return res
