Misapplications of the Wilcoxon-Mann-Whitney Test

Experimental designs using two or more treatments frequently arise in many fields of study, from medicine to psychology to policymaking. The use of rank-based nonparametric methods is recommended for analyzing effects in these designs as the observed data typically come from non-normal distributions with possibly several outliers. One of the most commonly used technique when conducting nonparametric analysis on two independent treatment groups is the Wilcoxon-Mann-Whitney (WMW) test, which is often thought of as a comparison between population medians of the two treatment groups. It can be shown that the WMW test actually fails as a comparison of medians and is better suited to be a comparison of stochastic superiority between these two groups