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Module « scipy.stats »

Fonction brunnermunzel - module scipy.stats

Signature de la fonction brunnermunzel

def brunnermunzel(x, y, alternative='two-sided', distribution='t', nan_policy='propagate', *, axis=0, keepdims=False) 

Description

help(scipy.stats.brunnermunzel)

    


Compute the Brunner-Munzel test on samples x and y.

The Brunner-Munzel test is a nonparametric test of the null hypothesis that
when values are taken one by one from each group, the probabilities of
getting large values in both groups are equal.
Unlike the Wilcoxon-Mann-Whitney's U test, this does not require the
assumption of equivariance of two groups. Note that this does not assume
the distributions are same. This test works on two independent samples,
which may have different sizes.

Parameters
----------
x, y : array_like
    Array of samples, should be one-dimensional.
alternative : {'two-sided', 'less', 'greater'}, optional
    Defines the alternative hypothesis.
    The following options are available (default is 'two-sided'):
    
      * 'two-sided'
      * 'less': one-sided
      * 'greater': one-sided
distribution : {'t', 'normal'}, optional
    Defines how to get the p-value.
    The following options are available (default is 't'):
    
      * 't': get the p-value by t-distribution
      * 'normal': get the p-value by standard normal distribution.
nan_policy : {'propagate', 'omit', 'raise'}
    Defines how to handle input NaNs.
    
    - ``propagate``: if a NaN is present in the axis slice (e.g. row) along
      which the  statistic is computed, the corresponding entry of the output
      will be NaN.
    - ``omit``: NaNs will be omitted when performing the calculation.
      If insufficient data remains in the axis slice along which the
      statistic is computed, the corresponding entry of the output will be
      NaN.
    - ``raise``: if a NaN is present, a ``ValueError`` will be raised.
axis : int or None, default: 0
    If an int, the axis of the input along which to compute the statistic.
    The statistic of each axis-slice (e.g. row) of the input will appear in a
    corresponding element of the output.
    If ``None``, the input will be raveled before computing the statistic.
keepdims : bool, default: False
    If this is set to True, the axes which are reduced are left
    in the result as dimensions with size one. With this option,
    the result will broadcast correctly against the input array.

Returns
-------
statistic : float
    The Brunner-Munzer W statistic.
pvalue : float
    p-value assuming an t distribution. One-sided or
    two-sided, depending on the choice of `alternative` and `distribution`.

See Also
--------

:func:`mannwhitneyu`
    Mann-Whitney rank test on two samples.


Notes
-----
Brunner and Munzel recommended to estimate the p-value by t-distribution
when the size of data is 50 or less. If the size is lower than 10, it would
be better to use permuted Brunner Munzel test (see [2]_).

Beginning in SciPy 1.9, ``np.matrix`` inputs (not recommended for new
code) are converted to ``np.ndarray`` before the calculation is performed. In
this case, the output will be a scalar or ``np.ndarray`` of appropriate shape
rather than a 2D ``np.matrix``. Similarly, while masked elements of masked
arrays are ignored, the output will be a scalar or ``np.ndarray`` rather than a
masked array with ``mask=False``.

References
----------
.. [1] Brunner, E. and Munzel, U. "The nonparametric Benhrens-Fisher
       problem: Asymptotic theory and a small-sample approximation".
       Biometrical Journal. Vol. 42(2000): 17-25.
.. [2] Neubert, K. and Brunner, E. "A studentized permutation test for the
       non-parametric Behrens-Fisher problem". Computational Statistics and
       Data Analysis. Vol. 51(2007): 5192-5204.

Examples
--------
>>> from scipy import stats
>>> x1 = [1,2,1,1,1,1,1,1,1,1,2,4,1,1]
>>> x2 = [3,3,4,3,1,2,3,1,1,5,4]
>>> w, p_value = stats.brunnermunzel(x1, x2)
>>> w
3.1374674823029505
>>> p_value
0.0057862086661515377

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