Module « scipy.stats »

Fonction levene - module scipy.stats

Signature de la fonction levene

def levene(*args, center='median', proportiontocut=0.05) 

Description

levene.__doc__

Perform Levene test for equal variances.

    The Levene test tests the null hypothesis that all input samples
    are from populations with equal variances.  Levene's test is an
    alternative to Bartlett's test `bartlett` in the case where
    there are significant deviations from normality.

    Parameters
    ----------
    sample1, sample2, ... : array_like
        The sample data, possibly with different lengths. Only one-dimensional
        samples are accepted.
    center : {'mean', 'median', 'trimmed'}, optional
        Which function of the data to use in the test.  The default
        is 'median'.
    proportiontocut : float, optional
        When `center` is 'trimmed', this gives the proportion of data points
        to cut from each end. (See `scipy.stats.trim_mean`.)
        Default is 0.05.

    Returns
    -------
    statistic : float
        The test statistic.
    pvalue : float
        The p-value for the test.

    Notes
    -----
    Three variations of Levene's test are possible.  The possibilities
    and their recommended usages are:

      * 'median' : Recommended for skewed (non-normal) distributions>
      * 'mean' : Recommended for symmetric, moderate-tailed distributions.
      * 'trimmed' : Recommended for heavy-tailed distributions.

    The test version using the mean was proposed in the original article
    of Levene ([2]_) while the median and trimmed mean have been studied by
    Brown and Forsythe ([3]_), sometimes also referred to as Brown-Forsythe
    test.

    References
    ----------
    .. [1] https://www.itl.nist.gov/div898/handbook/eda/section3/eda35a.htm
    .. [2] Levene, H. (1960). In Contributions to Probability and Statistics:
           Essays in Honor of Harold Hotelling, I. Olkin et al. eds.,
           Stanford University Press, pp. 278-292.
    .. [3] Brown, M. B. and Forsythe, A. B. (1974), Journal of the American
           Statistical Association, 69, 364-367

    Examples
    --------
    Test whether or not the lists `a`, `b` and `c` come from populations
    with equal variances.

    >>> from scipy.stats import levene
    >>> a = [8.88, 9.12, 9.04, 8.98, 9.00, 9.08, 9.01, 8.85, 9.06, 8.99]
    >>> b = [8.88, 8.95, 9.29, 9.44, 9.15, 9.58, 8.36, 9.18, 8.67, 9.05]
    >>> c = [8.95, 9.12, 8.95, 8.85, 9.03, 8.84, 9.07, 8.98, 8.86, 8.98]
    >>> stat, p = levene(a, b, c)
    >>> p
    0.002431505967249681

    The small p-value suggests that the populations do not have equal
    variances.

    This is not surprising, given that the sample variance of `b` is much
    larger than that of `a` and `c`:

    >>> [np.var(x, ddof=1) for x in [a, b, c]]
    [0.007054444444444413, 0.13073888888888888, 0.008890000000000002]