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Fonction boschloo_exact - module scipy.stats

Signature de la fonction boschloo_exact

def boschloo_exact(table, alternative='two-sided', n=32) 

Description

boschloo_exact.__doc__

Perform Boschloo's exact test on a 2x2 contingency table.

    Parameters
    ----------
    table : array_like of ints
        A 2x2 contingency table.  Elements should be non-negative integers.

    alternative : {'two-sided', 'less', 'greater'}, optional
        Defines the null and alternative hypotheses. Default is 'two-sided'.
        Please see explanations in the Notes section below.

    n : int, optional
        Number of sampling points used in the construction of the sampling
        method. Note that this argument will automatically be converted to
        the next higher power of 2 since `scipy.stats.qmc.Sobol` is used to
        select sample points. Default is 32. Must be positive. In most cases,
        32 points is enough to reach good precision. More points comes at
        performance cost.

    Returns
    -------
    ber : BoschlooExactResult
        A result object with the following attributes.

        statistic : float
            The statistic used in Boschloo's test; that is, the p-value
            from Fisher's exact test.

        pvalue : float
            P-value, the probability of obtaining a distribution at least as
            extreme as the one that was actually observed, assuming that the
            null hypothesis is true.

    See Also
    --------
    chi2_contingency : Chi-square test of independence of variables in a
        contingency table.
    fisher_exact : Fisher exact test on a 2x2 contingency table.
    barnard_exact : Barnard's exact test, which is a more powerful alternative
        than Fisher's exact test for 2x2 contingency tables.

    Notes
    -----
    Boschloo's test is an exact test used in the analysis of contingency
    tables. It examines the association of two categorical variables, and
    is a uniformly more powerful alternative to Fisher's exact test
    for 2x2 contingency tables.

    Let's define :math:`X_0` a 2x2 matrix representing the observed sample,
    where each column stores the binomial experiment, as in the example
    below. Let's also define :math:`p_1, p_2` the theoretical binomial
    probabilities for  :math:`x_{11}` and :math:`x_{12}`. When using
    Boschloo exact test, we can assert three different null hypotheses :

    - :math:`H_0 : p_1 \geq p_2` versus :math:`H_1 : p_1 < p_2`,
      with `alternative` = "less"

    - :math:`H_0 : p_1 \leq p_2` versus :math:`H_1 : p_1 > p_2`,
      with `alternative` = "greater"

    - :math:`H_0 : p_1 = p_2` versus :math:`H_1 : p_1 \neq p_2`,
      with `alternative` = "two-sided" (default one)

    Boschloo's exact test uses the p-value of Fisher's exact test as a 
    statistic, and Boschloo's p-value is the probability under the null 
    hypothesis of observing such an extreme value of this statistic.

    Boschloo's and Barnard's are both more powerful than Fisher's exact
    test.

    .. versionadded:: 1.7.0

    References
    ----------
    .. [1] R.D. Boschloo. "Raised conditional level of significance for the
       2 x 2-table when testing the equality of two probabilities",
       Statistica Neerlandica, 24(1), 1970

    .. [2] "Boschloo's test", Wikipedia,
       https://en.wikipedia.org/wiki/Boschloo%27s_test

    .. [3] Lise M. Saari et al. "Employee attitudes and job satisfaction",
       Human Resource Management, 43(4), 395-407, 2004,
       :doi:`10.1002/hrm.20032`.

    Examples
    --------
    In the following example, we consider the article "Employee
    attitudes and job satisfaction" [3]_
    which reports the results of a survey from 63 scientists and 117 college
    professors. Of the 63 scientists, 31 said they were very satisfied with
    their jobs, whereas 74 of the college professors were very satisfied
    with their work. Is this significant evidence that college
    professors are happier with their work than scientists?
    The following table summarizes the data mentioned above::

                         college professors   scientists
        Very Satisfied   74                     31
        Dissatisfied     43                     32

    When working with statistical hypothesis testing, we usually use a
    threshold probability or significance level upon which we decide
    to reject the null hypothesis :math:`H_0`. Suppose we choose the common
    significance level of 5%.

    Our alternative hypothesis is that college professors are truly more
    satisfied with their work than scientists. Therefore, we expect
    :math:`p_1` the proportion of very satisfied college professors to be
    greater than :math:`p_2`, the proportion of very satisfied scientists.
    We thus call `boschloo_exact` with the ``alternative="greater"`` option:

    >>> import scipy.stats as stats
    >>> res = stats.boschloo_exact([[74, 31], [43, 32]], alternative="greater")
    >>> res.statistic
    0.0483...
    >>> res.pvalue
    0.0355...

    Under the null hypothesis that scientists are happier in their work than
    college professors, the probability of obtaining test
    results at least as extreme as the observed data is approximately 3.55%.
    Since this p-value is less than our chosen significance level, we have
    evidence to reject :math:`H_0` in favor of the alternative hypothesis.