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Fonction anderson_ksamp - module scipy.stats

Signature de la fonction anderson_ksamp

def anderson_ksamp(samples, midrank=True) 

Description

anderson_ksamp.__doc__

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.

    Returns
    -------
    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%.
    significance_level : float
        An approximate significance level at which the null hypothesis for the
        provided samples can be rejected. The value is floored / capped at
        0.1% / 25%.

    Raises
    ------
    ValueError
        If less 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
    --------
    >>> from scipy import stats
    >>> rng = np.random.default_rng()

    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
    significance level of 3.2%:

    >>> stats.anderson_ksamp([rng.normal(size=50),
    ... rng.normal(loc=0.5, size=30)])
    (1.974403288713695,
      array([0.325, 1.226, 1.961, 2.718, 3.752, 4.592, 6.546]),
      0.04991293614572478)


    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 -0.731):

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