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Fonction wilcoxon - module scipy.stats

Signature de la fonction wilcoxon

def wilcoxon(x, y=None, zero_method='wilcox', correction=False, alternative='two-sided', mode='auto') 

Description

wilcoxon.__doc__

Calculate the Wilcoxon signed-rank test.

    The Wilcoxon signed-rank test tests the null hypothesis that two
    related paired samples come from the same distribution. In particular,
    it tests whether the distribution of the differences x - y is symmetric
    about zero. It is a non-parametric version of the paired T-test.

    Parameters
    ----------
    x : array_like
        Either the first set of measurements (in which case ``y`` is the second
        set of measurements), or the differences between two sets of
        measurements (in which case ``y`` is not to be specified.)  Must be
        one-dimensional.
    y : array_like, optional
        Either the second set of measurements (if ``x`` is the first set of
        measurements), or not specified (if ``x`` is the differences between
        two sets of measurements.)  Must be one-dimensional.
    zero_method : {"pratt", "wilcox", "zsplit"}, optional
        The following options are available (default is "wilcox"):

          * "pratt": Includes zero-differences in the ranking process,
            but drops the ranks of the zeros, see [4]_, (more conservative).
          * "wilcox": Discards all zero-differences, the default.
          * "zsplit": Includes zero-differences in the ranking process and
            split the zero rank between positive and negative ones.
    correction : bool, optional
        If True, apply continuity correction by adjusting the Wilcoxon rank
        statistic by 0.5 towards the mean value when computing the
        z-statistic if a normal approximation is used.  Default is False.
    alternative : {"two-sided", "greater", "less"}, optional
        The alternative hypothesis to be tested, see Notes. Default is
        "two-sided".
    mode : {"auto", "exact", "approx"}
        Method to calculate the p-value, see Notes. Default is "auto".

    Returns
    -------
    statistic : float
        If ``alternative`` is "two-sided", the sum of the ranks of the
        differences above or below zero, whichever is smaller.
        Otherwise the sum of the ranks of the differences above zero.
    pvalue : float
        The p-value for the test depending on ``alternative`` and ``mode``.

    See Also
    --------
    kruskal, mannwhitneyu

    Notes
    -----
    The test has been introduced in [4]_. Given n independent samples
    (xi, yi) from a bivariate distribution (i.e. paired samples),
    it computes the differences di = xi - yi. One assumption of the test
    is that the differences are symmetric, see [2]_.
    The two-sided test has the null hypothesis that the median of the
    differences is zero against the alternative that it is different from
    zero. The one-sided test has the null hypothesis that the median is
    positive against the alternative that it is negative
    (``alternative == 'less'``), or vice versa (``alternative == 'greater.'``).

    To derive the p-value, the exact distribution (``mode == 'exact'``)
    can be used for sample sizes of up to 25. The default ``mode == 'auto'``
    uses the exact distribution if there are at most 25 observations and no
    ties, otherwise a normal approximation is used (``mode == 'approx'``).

    The treatment of ties can be controlled by the parameter `zero_method`.
    If ``zero_method == 'pratt'``, the normal approximation is adjusted as in
    [5]_. A typical rule is to require that n > 20 ([2]_, p. 383).

    References
    ----------
    .. [1] https://en.wikipedia.org/wiki/Wilcoxon_signed-rank_test
    .. [2] Conover, W.J., Practical Nonparametric Statistics, 1971.
    .. [3] Pratt, J.W., Remarks on Zeros and Ties in the Wilcoxon Signed
       Rank Procedures, Journal of the American Statistical Association,
       Vol. 54, 1959, pp. 655-667. :doi:`10.1080/01621459.1959.10501526`
    .. [4] Wilcoxon, F., Individual Comparisons by Ranking Methods,
       Biometrics Bulletin, Vol. 1, 1945, pp. 80-83. :doi:`10.2307/3001968`
    .. [5] Cureton, E.E., The Normal Approximation to the Signed-Rank
       Sampling Distribution When Zero Differences are Present,
       Journal of the American Statistical Association, Vol. 62, 1967,
       pp. 1068-1069. :doi:`10.1080/01621459.1967.10500917`

    Examples
    --------
    In [4]_, the differences in height between cross- and self-fertilized
    corn plants is given as follows:

    >>> d = [6, 8, 14, 16, 23, 24, 28, 29, 41, -48, 49, 56, 60, -67, 75]

    Cross-fertilized plants appear to be be higher. To test the null
    hypothesis that there is no height difference, we can apply the
    two-sided test:

    >>> from scipy.stats import wilcoxon
    >>> w, p = wilcoxon(d)
    >>> w, p
    (24.0, 0.041259765625)

    Hence, we would reject the null hypothesis at a confidence level of 5%,
    concluding that there is a difference in height between the groups.
    To confirm that the median of the differences can be assumed to be
    positive, we use:

    >>> w, p = wilcoxon(d, alternative='greater')
    >>> w, p
    (96.0, 0.0206298828125)

    This shows that the null hypothesis that the median is negative can be
    rejected at a confidence level of 5% in favor of the alternative that
    the median is greater than zero. The p-values above are exact. Using the
    normal approximation gives very similar values:

    >>> w, p = wilcoxon(d, mode='approx')
    >>> w, p
    (24.0, 0.04088813291185591)

    Note that the statistic changed to 96 in the one-sided case (the sum
    of ranks of positive differences) whereas it is 24 in the two-sided
    case (the minimum of sum of ranks above and below zero).