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Fonction chi2_contingency - module scipy.stats

Signature de la fonction chi2_contingency

def chi2_contingency(observed, correction=True, lambda_=None) 

Description

chi2_contingency.__doc__

Chi-square test of independence of variables in a contingency table.

    This function computes the chi-square statistic and p-value for the
    hypothesis test of independence of the observed frequencies in the
    contingency table [1]_ `observed`.  The expected frequencies are computed
    based on the marginal sums under the assumption of independence; see
    `scipy.stats.contingency.expected_freq`.  The number of degrees of
    freedom is (expressed using numpy functions and attributes)::

        dof = observed.size - sum(observed.shape) + observed.ndim - 1


    Parameters
    ----------
    observed : array_like
        The contingency table. The table contains the observed frequencies
        (i.e. number of occurrences) in each category.  In the two-dimensional
        case, the table is often described as an "R x C table".
    correction : bool, optional
        If True, *and* the degrees of freedom is 1, apply Yates' correction
        for continuity.  The effect of the correction is to adjust each
        observed value by 0.5 towards the corresponding expected value.
    lambda_ : float or str, optional
        By default, the statistic computed in this test is Pearson's
        chi-squared statistic [2]_.  `lambda_` allows a statistic from the
        Cressie-Read power divergence family [3]_ to be used instead.  See
        `power_divergence` for details.

    Returns
    -------
    chi2 : float
        The test statistic.
    p : float
        The p-value of the test
    dof : int
        Degrees of freedom
    expected : ndarray, same shape as `observed`
        The expected frequencies, based on the marginal sums of the table.

    See Also
    --------
    contingency.expected_freq
    fisher_exact
    chisquare
    power_divergence
    barnard_exact
    boschloo_exact

    Notes
    -----
    An often quoted guideline for the validity of this calculation is that
    the test should be used only if the observed and expected frequencies
    in each cell are at least 5.

    This is a test for the independence of different categories of a
    population. The test is only meaningful when the dimension of
    `observed` is two or more.  Applying the test to a one-dimensional
    table will always result in `expected` equal to `observed` and a
    chi-square statistic equal to 0.

    This function does not handle masked arrays, because the calculation
    does not make sense with missing values.

    Like stats.chisquare, this function computes a chi-square statistic;
    the convenience this function provides is to figure out the expected
    frequencies and degrees of freedom from the given contingency table.
    If these were already known, and if the Yates' correction was not
    required, one could use stats.chisquare.  That is, if one calls::

        chi2, p, dof, ex = chi2_contingency(obs, correction=False)

    then the following is true::

        (chi2, p) == stats.chisquare(obs.ravel(), f_exp=ex.ravel(),
                                     ddof=obs.size - 1 - dof)

    The `lambda_` argument was added in version 0.13.0 of scipy.

    References
    ----------
    .. [1] "Contingency table",
           https://en.wikipedia.org/wiki/Contingency_table
    .. [2] "Pearson's chi-squared test",
           https://en.wikipedia.org/wiki/Pearson%27s_chi-squared_test
    .. [3] Cressie, N. and Read, T. R. C., "Multinomial Goodness-of-Fit
           Tests", J. Royal Stat. Soc. Series B, Vol. 46, No. 3 (1984),
           pp. 440-464.

    Examples
    --------
    A two-way example (2 x 3):

    >>> from scipy.stats import chi2_contingency
    >>> obs = np.array([[10, 10, 20], [20, 20, 20]])
    >>> chi2_contingency(obs)
    (2.7777777777777777,
     0.24935220877729619,
     2,
     array([[ 12.,  12.,  16.],
            [ 18.,  18.,  24.]]))

    Perform the test using the log-likelihood ratio (i.e. the "G-test")
    instead of Pearson's chi-squared statistic.

    >>> g, p, dof, expctd = chi2_contingency(obs, lambda_="log-likelihood")
    >>> g, p
    (2.7688587616781319, 0.25046668010954165)

    A four-way example (2 x 2 x 2 x 2):

    >>> obs = np.array(
    ...     [[[[12, 17],
    ...        [11, 16]],
    ...       [[11, 12],
    ...        [15, 16]]],
    ...      [[[23, 15],
    ...        [30, 22]],
    ...       [[14, 17],
    ...        [15, 16]]]])
    >>> chi2_contingency(obs)
    (8.7584514426741897,
     0.64417725029295503,
     11,
     array([[[[ 14.15462386,  14.15462386],
              [ 16.49423111,  16.49423111]],
             [[ 11.2461395 ,  11.2461395 ],
              [ 13.10500554,  13.10500554]]],
            [[[ 19.5591166 ,  19.5591166 ],
              [ 22.79202844,  22.79202844]],
             [[ 15.54012004,  15.54012004],
              [ 18.10873492,  18.10873492]]]]))