Choice of effect size for Mann-Whitney/Wilcoxon tests

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by rconroy » Thu May 20, 2021 6:39 pm

The Wilcoxon Mann-Whitney test has an inbuilt measure of effect size! If you look at the title of Mann and Whitney's original paper, it's clear :

1.Mann, H. B. & Whitney, D. R. On a Test of Whether one of Two Random Variables is Stochastically Larger than the Other. Ann. Math. Statist. 18, 50–60 (1947).

You can calculate that probability very simply from the value of U. Divide U by its maximum value, which is N1*N2 and you have the probability that an observation from group 1 will be higher than an observation from group 2.

This is sometimes called the common language effect size, and sometimes (mistakenly) Harrell's c (which is a special case of it).
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