pingouin.mwu

pingouin.mwu(x, y, tail='two-sided')[source]

Mann-Whitney U Test (= Wilcoxon rank-sum test). It is the non-parametric version of the independent T-test.

Parameters
x, yarray_like

First and second set of observations. x and y must be independent.

tailstring

Specify whether to return ‘one-sided’ or ‘two-sided’ p-value. Can also be ‘greater’ or ‘less’ to specify the direction of the test. If tail='one-sided', the alternative of the test will be automatically detected by comparing the medians of x and y. For instance, if median(x) < median(y) and tail='one-sided', Pingouin will automatically set tail='less', and vice versa.

Returns
statspandas DataFrame

Test summary

'U-val' : U-value
'p-val' : p-value
'RBC'   : rank-biserial correlation (effect size)
'CLES'  : common language effect size

Notes

The Mann–Whitney U test (also called Wilcoxon rank-sum test) is a non-parametric test of the null hypothesis that it is equally likely that a randomly selected value from one sample will be less than or greater than a randomly selected value from a second sample. The test assumes that the two samples are independent. This test corrects for ties and by default uses a continuity correction (see scipy.stats.mannwhitneyu() for details).

The rank biserial correlation effect size is the difference between the proportion of favorable evidence minus the proportion of unfavorable evidence (see Kerby 2014).

The common language effect size is the probability (from 0 to 1) that a randomly selected observation from the first sample will be greater than a randomly selected observation from the second sample.

References

1

Mann, H. B., & Whitney, D. R. (1947). On a test of whether one of two random variables is stochastically larger than the other. The annals of mathematical statistics, 50-60.

2

Kerby, D. S. (2014). The simple difference formula: An approach to teaching nonparametric correlation. Comprehensive Psychology, 3, 11-IT.

3

McGraw, K. O., & Wong, S. P. (1992). A common language effect size statistic. Psychological bulletin, 111(2), 361.

Examples

>>> import numpy as np
>>> import pingouin as pg
>>> np.random.seed(123)
>>> x = np.random.uniform(low=0, high=1, size=20)
>>> y = np.random.uniform(low=0.2, high=1.2, size=20)
>>> pg.mwu(x, y, tail='two-sided')
     U-val       tail    p-val    RBC   CLES
MWU   97.0  two-sided  0.00556  0.515  0.758

Compare with SciPy

>>> import scipy
>>> scipy.stats.mannwhitneyu(x, y, use_continuity=True,
...                          alternative='two-sided')
MannwhitneyuResult(statistic=97.0, pvalue=0.0055604599321374135)

One-sided tail: one can either manually specify the alternative hypothesis

>>> pg.mwu(x, y, tail='greater')
     U-val     tail     p-val    RBC   CLES
MWU   97.0  greater  0.997442  0.515  0.758
>>> pg.mwu(x, y, tail='less')
     U-val  tail    p-val    RBC   CLES
MWU   97.0  less  0.00278  0.515  0.758

Or simply leave it to Pingouin, using the ‘one-sided’ argument, in which case Pingouin will compare the medians of x and y and select the most appropriate tail based on that:

>>> # Since np.median(x) < np.median(y), this is equivalent to tail='less'
>>> pg.mwu(x, y, tail='one-sided')
     U-val  tail    p-val    RBC   CLES
MWU   97.0  less  0.00278  0.515  0.758