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bundles / scipy latest / scipy / stats / _stats_py / brunnermunzel

function

scipy.stats._stats_py:brunnermunzel

source: /scipy/stats/_stats_py.py :8604

Signature

def   brunnermunzel ( x ,  y ,  alternative = two-sided ,  distribution = t ,  nan_policy = propagate ,  * ,  axis = 0 ,  keepdims = False )

Summary

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

Extended Summary

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.

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.

Array API Standard Support

brunnermunzel has experimental support for Python Array API Standard compatible backends in addition to NumPy. Please consider testing these features by setting an environment variable SCIPY_ARRAY_API=1 and providing CuPy, PyTorch, JAX, or Dask arrays as array arguments. The following combinations of backend and device (or other capability) are supported.

====================  ====================  ====================
Library               CPU                   GPU
====================  ====================  ====================
NumPy                 ✅                     n/a                 
CuPy                  n/a                   ⛔                   
PyTorch               ✅                     ⛔                   
JAX                   ⛔                     ⛔                   
Dask                  ⛔                     n/a                 
====================  ====================  ====================

See dev-arrayapi for more information.

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
p_value
✗

See also

mannwhitneyu

Mann-Whitney rank test on two samples.

Aliases

  • scipy.stats.brunnermunzel

Referenced by

This package