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Fonction combine_pvalues - module scipy.stats

Signature de la fonction combine_pvalues

def combine_pvalues(pvalues, method='fisher', weights=None) 

Description

combine_pvalues.__doc__

    Combine p-values from independent tests bearing upon the same hypothesis.

    Parameters
    ----------
    pvalues : array_like, 1-D
        Array of p-values assumed to come from independent tests.
    method : {'fisher', 'pearson', 'tippett', 'stouffer',
              'mudholkar_george'}, optional

        Name of method to use to combine p-values.
        The following methods are available (default is 'fisher'):

          * 'fisher': Fisher's method (Fisher's combined probability test), the
            sum of the logarithm of the p-values
          * 'pearson': Pearson's method (similar to Fisher's but uses sum of the
            complement of the p-values inside the logarithms)
          * 'tippett': Tippett's method (minimum of p-values)
          * 'stouffer': Stouffer's Z-score method
          * 'mudholkar_george': the difference of Fisher's and Pearson's methods
            divided by 2
    weights : array_like, 1-D, optional
        Optional array of weights used only for Stouffer's Z-score method.

    Returns
    -------
    statistic: float
        The statistic calculated by the specified method.
    pval: float
        The combined p-value.

    Notes
    -----
    Fisher's method (also known as Fisher's combined probability test) [1]_ uses
    a chi-squared statistic to compute a combined p-value. The closely related
    Stouffer's Z-score method [2]_ uses Z-scores rather than p-values. The
    advantage of Stouffer's method is that it is straightforward to introduce
    weights, which can make Stouffer's method more powerful than Fisher's
    method when the p-values are from studies of different size [6]_ [7]_.
    The Pearson's method uses :math:`log(1-p_i)` inside the sum whereas Fisher's
    method uses :math:`log(p_i)` [4]_. For Fisher's and Pearson's method, the
    sum of the logarithms is multiplied by -2 in the implementation. This
    quantity has a chi-square distribution that determines the p-value. The
    `mudholkar_george` method is the difference of the Fisher's and Pearson's
    test statistics, each of which include the -2 factor [4]_. However, the
    `mudholkar_george` method does not include these -2 factors. The test
    statistic of `mudholkar_george` is the sum of logisitic random variables and
    equation 3.6 in [3]_ is used to approximate the p-value based on Student's
    t-distribution.

    Fisher's method may be extended to combine p-values from dependent tests
    [5]_. Extensions such as Brown's method and Kost's method are not currently
    implemented.

    .. versionadded:: 0.15.0

    References
    ----------
    .. [1] https://en.wikipedia.org/wiki/Fisher%27s_method
    .. [2] https://en.wikipedia.org/wiki/Fisher%27s_method#Relation_to_Stouffer.27s_Z-score_method
    .. [3] George, E. O., and G. S. Mudholkar. "On the convolution of logistic
           random variables." Metrika 30.1 (1983): 1-13.
    .. [4] Heard, N. and Rubin-Delanchey, P. "Choosing between methods of
           combining p-values."  Biometrika 105.1 (2018): 239-246.
    .. [5] Whitlock, M. C. "Combining probability from independent tests: the
           weighted Z-method is superior to Fisher's approach." Journal of
           Evolutionary Biology 18, no. 5 (2005): 1368-1373.
    .. [6] Zaykin, Dmitri V. "Optimally weighted Z-test is a powerful method
           for combining probabilities in meta-analysis." Journal of
           Evolutionary Biology 24, no. 8 (2011): 1836-1841.
    .. [7] https://en.wikipedia.org/wiki/Extensions_of_Fisher%27s_method