pingouin.mwu

pingouin.
mwu
(x, y, tail='twosided')[source] MannWhitney U Test (= Wilcoxon ranksum test). It is the nonparametric version of the independent Ttest.
 Parameters
 x, yarray_like
First and second set of observations.
x
andy
must be independent. tailstring
Specify whether to return ‘onesided’ or ‘twosided’ pvalue. Can also be ‘greater’ or ‘less’ to specify the direction of the test. If
tail='onesided'
, the alternative of the test will be automatically detected by comparing the medians ofx
andy
. For instance, if median(x
) < median(y
) andtail='onesided'
, Pingouin will automatically settail='less'
, and vice versa.
 Returns
 statspandas DataFrame
Test summary
'Uval' : Uvalue 'pval' : pvalue 'RBC' : rankbiserial correlation (effect size) 'CLES' : common language effect size
See also
Notes
The Mann–Whitney U test (also called Wilcoxon ranksum test) is a nonparametric 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, 5060.
 2
Kerby, D. S. (2014). The simple difference formula: An approach to teaching nonparametric correlation. Comprehensive Psychology, 3, 11IT.
 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='twosided') Uval tail pval RBC CLES MWU 97.0 twosided 0.00556 0.515 0.758
Compare with SciPy
>>> import scipy >>> scipy.stats.mannwhitneyu(x, y, use_continuity=True, ... alternative='twosided') MannwhitneyuResult(statistic=97.0, pvalue=0.0055604599321374135)
Onesided tail: one can either manually specify the alternative hypothesis
>>> pg.mwu(x, y, tail='greater') Uval tail pval RBC CLES MWU 97.0 greater 0.997442 0.515 0.758
>>> pg.mwu(x, y, tail='less') Uval tail pval RBC CLES MWU 97.0 less 0.00278 0.515 0.758
Or simply leave it to Pingouin, using the ‘onesided’ argument, in which case Pingouin will compare the medians of
x
andy
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='onesided') Uval tail pval RBC CLES MWU 97.0 less 0.00278 0.515 0.758