Module « scipy.stats »

Fonction spearmanr - module scipy.stats

Signature de la fonction spearmanr

def spearmanr(a, b=None, axis=0, nan_policy='propagate', alternative='two-sided') 

Description

spearmanr.__doc__

Calculate a Spearman correlation coefficient with associated p-value.

    The Spearman rank-order correlation coefficient is a nonparametric measure
    of the monotonicity of the relationship between two datasets. Unlike the
    Pearson correlation, the Spearman correlation does not assume that both
    datasets are normally distributed. Like other correlation coefficients,
    this one varies between -1 and +1 with 0 implying no correlation.
    Correlations of -1 or +1 imply an exact monotonic relationship. Positive
    correlations imply that as x increases, so does y. Negative correlations
    imply that as x increases, y decreases.

    The p-value roughly indicates the probability of an uncorrelated system
    producing datasets that have a Spearman correlation at least as extreme
    as the one computed from these datasets. The p-values are not entirely
    reliable but are probably reasonable for datasets larger than 500 or so.

    Parameters
    ----------
    a, b : 1D or 2D array_like, b is optional
        One or two 1-D or 2-D arrays containing multiple variables and
        observations. When these are 1-D, each represents a vector of
        observations of a single variable. For the behavior in the 2-D case,
        see under ``axis``, below.
        Both arrays need to have the same length in the ``axis`` dimension.
    axis : int or None, optional
        If axis=0 (default), then each column represents a variable, with
        observations in the rows. If axis=1, the relationship is transposed:
        each row represents a variable, while the columns contain observations.
        If axis=None, then both arrays will be raveled.
    nan_policy : {'propagate', 'raise', 'omit'}, optional
        Defines how to handle when input contains nan.
        The following options are available (default is 'propagate'):

        * 'propagate': returns nan
        * 'raise': throws an error
        * 'omit': performs the calculations ignoring nan values

    alternative : {'two-sided', 'less', 'greater'}, optional
        Defines the alternative hypothesis. Default is 'two-sided'.
        The following options are available:

        * 'two-sided': the correlation is nonzero
        * 'less': the correlation is negative (less than zero)
        * 'greater':  the correlation is positive (greater than zero)

        .. versionadded:: 1.7.0

    Returns
    -------
    correlation : float or ndarray (2-D square)
        Spearman correlation matrix or correlation coefficient (if only 2
        variables are given as parameters. Correlation matrix is square with
        length equal to total number of variables (columns or rows) in ``a``
        and ``b`` combined.
    pvalue : float
        The p-value for a hypothesis test whose null hypotheisis
        is that two sets of data are uncorrelated. See `alternative` above
        for alternative hypotheses. `pvalue` has the same
        shape as `correlation`.

    References
    ----------
    .. [1] Zwillinger, D. and Kokoska, S. (2000). CRC Standard
       Probability and Statistics Tables and Formulae. Chapman & Hall: New
       York. 2000.
       Section  14.7

    Examples
    --------
    >>> from scipy import stats
    >>> stats.spearmanr([1,2,3,4,5], [5,6,7,8,7])
    SpearmanrResult(correlation=0.82078..., pvalue=0.08858...)
    >>> rng = np.random.default_rng()
    >>> x2n = rng.standard_normal((100, 2))
    >>> y2n = rng.standard_normal((100, 2))
    >>> stats.spearmanr(x2n)
    SpearmanrResult(correlation=-0.07960396039603959, pvalue=0.4311168705769747)
    >>> stats.spearmanr(x2n[:,0], x2n[:,1])
    SpearmanrResult(correlation=-0.07960396039603959, pvalue=0.4311168705769747)
    >>> rho, pval = stats.spearmanr(x2n, y2n)
    >>> rho
    array([[ 1.        , -0.07960396, -0.08314431,  0.09662166],
           [-0.07960396,  1.        , -0.14448245,  0.16738074],
           [-0.08314431, -0.14448245,  1.        ,  0.03234323],
           [ 0.09662166,  0.16738074,  0.03234323,  1.        ]])
    >>> pval
    array([[0.        , 0.43111687, 0.41084066, 0.33891628],
           [0.43111687, 0.        , 0.15151618, 0.09600687],
           [0.41084066, 0.15151618, 0.        , 0.74938561],
           [0.33891628, 0.09600687, 0.74938561, 0.        ]])
    >>> rho, pval = stats.spearmanr(x2n.T, y2n.T, axis=1)
    >>> rho
    array([[ 1.        , -0.07960396, -0.08314431,  0.09662166],
           [-0.07960396,  1.        , -0.14448245,  0.16738074],
           [-0.08314431, -0.14448245,  1.        ,  0.03234323],
           [ 0.09662166,  0.16738074,  0.03234323,  1.        ]])
    >>> stats.spearmanr(x2n, y2n, axis=None)
    SpearmanrResult(correlation=0.044981624540613524, pvalue=0.5270803651336189)
    >>> stats.spearmanr(x2n.ravel(), y2n.ravel())
    SpearmanrResult(correlation=0.044981624540613524, pvalue=0.5270803651336189)

    >>> rng = np.random.default_rng()
    >>> xint = rng.integers(10, size=(100, 2))
    >>> stats.spearmanr(xint)
    SpearmanrResult(correlation=0.09800224850707953, pvalue=0.3320271757932076)