Module « scipy.stats »

Fonction ks_2samp - module scipy.stats

Signature de la fonction ks_2samp

def ks_2samp(data1, data2, alternative='two-sided', mode='auto') 

Description

ks_2samp.__doc__

    Performs the two-sample Kolmogorov-Smirnov test for goodness of fit.

    This test compares the underlying continuous distributions F(x) and G(x)
    of two independent samples.  See Notes for a description
    of the available null and alternative hypotheses.

    Parameters
    ----------
    data1, data2 : array_like, 1-Dimensional
        Two arrays of sample observations assumed to be drawn from a continuous
        distribution, sample sizes can be different.
    alternative : {'two-sided', 'less', 'greater'}, optional
        Defines the null and alternative hypotheses. Default is 'two-sided'.
        Please see explanations in the Notes below.
    mode : {'auto', 'exact', 'asymp'}, optional
        Defines the method used for calculating the p-value.
        The following options are available (default is 'auto'):

          * 'auto' : use 'exact' for small size arrays, 'asymp' for large
          * 'exact' : use exact distribution of test statistic
          * 'asymp' : use asymptotic distribution of test statistic

    Returns
    -------
    statistic : float
        KS statistic.
    pvalue : float
        One-tailed or two-tailed p-value.

    See Also
    --------
    kstest, ks_1samp, epps_singleton_2samp, anderson_ksamp

    Notes
    -----
    There are three options for the null and corresponding alternative
    hypothesis that can be selected using the `alternative` parameter.

    - `two-sided`: The null hypothesis is that the two distributions are
      identical, F(x)=G(x) for all x; the alternative is that they are not
      identical.

    - `less`: The null hypothesis is that F(x) >= G(x) for all x; the
      alternative is that F(x) < G(x) for at least one x.

    - `greater`: The null hypothesis is that F(x) <= G(x) for all x; the
      alternative is that F(x) > G(x) for at least one x.

    Note that the alternative hypotheses describe the *CDFs* of the
    underlying distributions, not the observed values. For example,
    suppose x1 ~ F and x2 ~ G. If F(x) > G(x) for all x, the values in
    x1 tend to be less than those in x2.


    If the KS statistic is small or the p-value is high, then we cannot
    reject the null hypothesis in favor of the alternative.

    If the mode is 'auto', the computation is exact if the sample sizes are
    less than 10000.  For larger sizes, the computation uses the
    Kolmogorov-Smirnov distributions to compute an approximate value.

    The 'two-sided' 'exact' computation computes the complementary probability
    and then subtracts from 1.  As such, the minimum probability it can return
    is about 1e-16.  While the algorithm itself is exact, numerical
    errors may accumulate for large sample sizes.   It is most suited to
    situations in which one of the sample sizes is only a few thousand.

    We generally follow Hodges' treatment of Drion/Gnedenko/Korolyuk [1]_.

    References
    ----------
    .. [1] Hodges, J.L. Jr.,  "The Significance Probability of the Smirnov
           Two-Sample Test," Arkiv fiur Matematik, 3, No. 43 (1958), 469-86.

    Examples
    --------
    >>> from scipy import stats
    >>> rng = np.random.default_rng()

    >>> n1 = 200  # size of first sample
    >>> n2 = 300  # size of second sample

    For a different distribution, we can reject the null hypothesis since the
    pvalue is below 1%:

    >>> rvs1 = stats.norm.rvs(size=n1, loc=0., scale=1, random_state=rng)
    >>> rvs2 = stats.norm.rvs(size=n2, loc=0.5, scale=1.5, random_state=rng)
    >>> stats.ks_2samp(rvs1, rvs2)
     KstestResult(statistic=0.24833333333333332, pvalue=5.846586728086578e-07)

    For a slightly different distribution, we cannot reject the null hypothesis
    at a 10% or lower alpha since the p-value at 0.144 is higher than 10%

    >>> rvs3 = stats.norm.rvs(size=n2, loc=0.01, scale=1.0, random_state=rng)
    >>> stats.ks_2samp(rvs1, rvs3)
    KstestResult(statistic=0.07833333333333334, pvalue=0.4379658456442945)

    For an identical distribution, we cannot reject the null hypothesis since
    the p-value is high, 41%:

    >>> rvs4 = stats.norm.rvs(size=n2, loc=0.0, scale=1.0, random_state=rng)
    >>> stats.ks_2samp(rvs1, rvs4)
    KstestResult(statistic=0.12166666666666667, pvalue=0.05401863039081145)