`scipy.stats._stats_py:ranksums`

source: /scipy/stats/_stats_py.py :8306

Signature

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

Summary

Compute the Wilcoxon rank-sum statistic for two samples.

Extended Summary

The Wilcoxon rank-sum test tests the null hypothesis that two sets of measurements are drawn from the same distribution. The alternative hypothesis is that values in one sample are more likely to be larger than the values in the other sample.

This test should be used to compare two samples from continuous distributions. It does not handle ties between measurements in x and y. For tie-handling and an optional continuity correction see scipy.stats.mannwhitneyu.

Parameters

x,y : array_like

The data from the two samples.

alternative : {'two-sided', 'less', 'greater'}, optional

Defines the alternative hypothesis. Default is 'two-sided'. The following options are available:

'two-sided': one of the distributions (underlying x or y) is stochastically greater than the other.
'less': the distribution underlying x is stochastically less than the distribution underlying y.
'greater': the distribution underlying x is stochastically greater than the distribution underlying y.

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.

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.

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 test statistic under the large-sample approximation that the rank sum statistic is normally distributed.
pvalue : float: The p-value of the test.

Notes

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

ranksums 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

We can test the hypothesis that two independent unequal-sized samples are drawn from the same distribution with computing the Wilcoxon rank-sum statistic.

import numpy as np
from scipy.stats import ranksums
rng = np.random.default_rng()
sample1 = rng.uniform(-1, 1, 200)
sample2 = rng.uniform(-0.5, 1.5, 300) # a shifted distribution

✓

ranksums(sample1, sample2)
ranksums(sample1, sample2, alternative='less')
ranksums(sample1, sample2, alternative='greater')

✗

The p-value of less than ``0.05`` indicates that this test rejects the hypothesis at the 5% significance level.

Aliases

scipy.stats.ranksums