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Module « scipy.stats »

Fonction anderson_ksamp - module scipy.stats

Signature de la fonction anderson_ksamp

def anderson_ksamp(samples, midrank=True, *, method=None) 

Description

help(scipy.stats.anderson_ksamp)

The Anderson-Darling test for k-samples.

The k-sample Anderson-Darling test is a modification of the
one-sample Anderson-Darling test. It tests the null hypothesis
that k-samples are drawn from the same population without having
to specify the distribution function of that population. The
critical values depend on the number of samples.

Parameters
----------
samples : sequence of 1-D array_like
    Array of sample data in arrays.
midrank : bool, optional
    Type of Anderson-Darling test which is computed. Default
    (True) is the midrank test applicable to continuous and
    discrete populations. If False, the right side empirical
    distribution is used.
method : PermutationMethod, optional
    Defines the method used to compute the p-value. If `method` is an
    instance of `PermutationMethod`, the p-value is computed using
    `scipy.stats.permutation_test` with the provided configuration options
    and other appropriate settings. Otherwise, the p-value is interpolated
    from tabulated values.

Returns
-------
res : Anderson_ksampResult
    An object containing attributes:

    statistic : float
        Normalized k-sample Anderson-Darling test statistic.
    critical_values : array
        The critical values for significance levels 25%, 10%, 5%, 2.5%, 1%,
        0.5%, 0.1%.
    pvalue : float
        The approximate p-value of the test. If `method` is not
        provided, the value is floored / capped at 0.1% / 25%.

Raises
------
ValueError
    If fewer than 2 samples are provided, a sample is empty, or no
    distinct observations are in the samples.

See Also
--------
ks_2samp : 2 sample Kolmogorov-Smirnov test
anderson : 1 sample Anderson-Darling test

Notes
-----
[1]_ defines three versions of the k-sample Anderson-Darling test:
one for continuous distributions and two for discrete
distributions, in which ties between samples may occur. The
default of this routine is to compute the version based on the
midrank empirical distribution function. This test is applicable
to continuous and discrete data. If midrank is set to False, the
right side empirical distribution is used for a test for discrete
data. According to [1]_, the two discrete test statistics differ
only slightly if a few collisions due to round-off errors occur in
the test not adjusted for ties between samples.

The critical values corresponding to the significance levels from 0.01
to 0.25 are taken from [1]_. p-values are floored / capped
at 0.1% / 25%. Since the range of critical values might be extended in
future releases, it is recommended not to test ``p == 0.25``, but rather
``p >= 0.25`` (analogously for the lower bound).

.. versionadded:: 0.14.0

References
----------
.. [1] Scholz, F. W and Stephens, M. A. (1987), K-Sample
       Anderson-Darling Tests, Journal of the American Statistical
       Association, Vol. 82, pp. 918-924.

Examples
--------
>>> import numpy as np
>>> from scipy import stats
>>> rng = np.random.default_rng()
>>> res = stats.anderson_ksamp([rng.normal(size=50),
... rng.normal(loc=0.5, size=30)])
>>> res.statistic, res.pvalue
(1.974403288713695, 0.04991293614572478)
>>> res.critical_values
array([0.325, 1.226, 1.961, 2.718, 3.752, 4.592, 6.546])

The null hypothesis that the two random samples come from the same
distribution can be rejected at the 5% level because the returned
test value is greater than the critical value for 5% (1.961) but
not at the 2.5% level. The interpolation gives an approximate
p-value of 4.99%.

>>> samples = [rng.normal(size=50), rng.normal(size=30),
...            rng.normal(size=20)]
>>> res = stats.anderson_ksamp(samples)
>>> res.statistic, res.pvalue
(-0.29103725200789504, 0.25)
>>> res.critical_values
array([ 0.44925884,  1.3052767 ,  1.9434184 ,  2.57696569,  3.41634856,
  4.07210043, 5.56419101])

The null hypothesis cannot be rejected for three samples from an
identical distribution. The reported p-value (25%) has been capped and
may not be very accurate (since it corresponds to the value 0.449
whereas the statistic is -0.291).

In such cases where the p-value is capped or when sample sizes are
small, a permutation test may be more accurate.

>>> method = stats.PermutationMethod(n_resamples=9999, random_state=rng)
>>> res = stats.anderson_ksamp(samples, method=method)
>>> res.pvalue
0.5254

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