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Fonction chisquare - module scipy.stats

Signature de la fonction chisquare

def chisquare(f_obs, f_exp=None, ddof=0, axis=0) 

Description

chisquare.__doc__

Calculate a one-way chi-square test.

    The chi-square test tests the null hypothesis that the categorical data
    has the given frequencies.

    Parameters
    ----------
    f_obs : array_like
        Observed frequencies in each category.
    f_exp : array_like, optional
        Expected frequencies in each category.  By default the categories are
        assumed to be equally likely.
    ddof : int, optional
        "Delta degrees of freedom": adjustment to the degrees of freedom
        for the p-value.  The p-value is computed using a chi-squared
        distribution with ``k - 1 - ddof`` degrees of freedom, where `k`
        is the number of observed frequencies.  The default value of `ddof`
        is 0.
    axis : int or None, optional
        The axis of the broadcast result of `f_obs` and `f_exp` along which to
        apply the test.  If axis is None, all values in `f_obs` are treated
        as a single data set.  Default is 0.

    Returns
    -------
    chisq : float or ndarray
        The chi-squared test statistic.  The value is a float if `axis` is
        None or `f_obs` and `f_exp` are 1-D.
    p : float or ndarray
        The p-value of the test.  The value is a float if `ddof` and the
        return value `chisq` are scalars.

    See Also
    --------
    scipy.stats.power_divergence
    scipy.stats.fisher_exact : Fisher exact test on a 2x2 contingency table.
    scipy.stats.barnard_exact : An unconditional exact test. An alternative
        to chi-squared test for small sample sizes.

    Notes
    -----
    This test is invalid when the observed or expected frequencies in each
    category are too small.  A typical rule is that all of the observed
    and expected frequencies should be at least 5. According to [3]_, the
    total number of samples is recommended to be greater than 13,
    otherwise exact tests (such as Barnard's Exact test) should be used
    because they do not overreject.

    Also, the sum of the observed and expected frequencies must be the same
    for the test to be valid; `chisquare` raises an error if the sums do not
    agree within a relative tolerance of ``1e-8``.

    The default degrees of freedom, k-1, are for the case when no parameters
    of the distribution are estimated. If p parameters are estimated by
    efficient maximum likelihood then the correct degrees of freedom are
    k-1-p. If the parameters are estimated in a different way, then the
    dof can be between k-1-p and k-1. However, it is also possible that
    the asymptotic distribution is not chi-square, in which case this test
    is not appropriate.

    References
    ----------
    .. [1] Lowry, Richard.  "Concepts and Applications of Inferential
           Statistics". Chapter 8.
           https://web.archive.org/web/20171022032306/http://vassarstats.net:80/textbook/ch8pt1.html
    .. [2] "Chi-squared test", https://en.wikipedia.org/wiki/Chi-squared_test
    .. [3] Pearson, Karl. "On the criterion that a given system of deviations from the probable
           in the case of a correlated system of variables is such that it can be reasonably
           supposed to have arisen from random sampling", Philosophical Magazine. Series 5. 50
           (1900), pp. 157-175.

    Examples
    --------
    When just `f_obs` is given, it is assumed that the expected frequencies
    are uniform and given by the mean of the observed frequencies.

    >>> from scipy.stats import chisquare
    >>> chisquare([16, 18, 16, 14, 12, 12])
    (2.0, 0.84914503608460956)

    With `f_exp` the expected frequencies can be given.

    >>> chisquare([16, 18, 16, 14, 12, 12], f_exp=[16, 16, 16, 16, 16, 8])
    (3.5, 0.62338762774958223)

    When `f_obs` is 2-D, by default the test is applied to each column.

    >>> obs = np.array([[16, 18, 16, 14, 12, 12], [32, 24, 16, 28, 20, 24]]).T
    >>> obs.shape
    (6, 2)
    >>> chisquare(obs)
    (array([ 2.        ,  6.66666667]), array([ 0.84914504,  0.24663415]))

    By setting ``axis=None``, the test is applied to all data in the array,
    which is equivalent to applying the test to the flattened array.

    >>> chisquare(obs, axis=None)
    (23.31034482758621, 0.015975692534127565)
    >>> chisquare(obs.ravel())
    (23.31034482758621, 0.015975692534127565)

    `ddof` is the change to make to the default degrees of freedom.

    >>> chisquare([16, 18, 16, 14, 12, 12], ddof=1)
    (2.0, 0.73575888234288467)

    The calculation of the p-values is done by broadcasting the
    chi-squared statistic with `ddof`.

    >>> chisquare([16, 18, 16, 14, 12, 12], ddof=[0,1,2])
    (2.0, array([ 0.84914504,  0.73575888,  0.5724067 ]))

    `f_obs` and `f_exp` are also broadcast.  In the following, `f_obs` has
    shape (6,) and `f_exp` has shape (2, 6), so the result of broadcasting
    `f_obs` and `f_exp` has shape (2, 6).  To compute the desired chi-squared
    statistics, we use ``axis=1``:

    >>> chisquare([16, 18, 16, 14, 12, 12],
    ...           f_exp=[[16, 16, 16, 16, 16, 8], [8, 20, 20, 16, 12, 12]],
    ...           axis=1)
    (array([ 3.5 ,  9.25]), array([ 0.62338763,  0.09949846]))