Psychologists Should Use Brunner-Munzel’s Instead of Mann-Whitney’s <i>U</i> Test as the Default Nonparametric Procedure

Abstract

To investigate whether a variable tends to be larger in one population than in another, the t test is the standard procedure. In some situations, the parametric t test is inappropriate, and a nonparametric procedure should be used instead. The default nonparametric procedure is Mann-Whitney’s U test. Despite being a nonparametric test, Mann-Whitney’s test is associated with a strong assumption, known as exchangeability. I demonstrate that if exchangeability is violated, Mann-Whitney’s test can lead to wrong statistical inferences even for large samples. In addition, I argue that in psychology, exchangeability is typically not met. As a remedy, I introduce Brunner-Munzel’s test and demonstrate that it provides good Type I error rate control even if exchangeability is not met and that it has similar power as Mann-Whitney’s test. Consequently, I recommend using Brunner-Munzel’s test by default. To facilitate this, I provide advice on how to perform and report on Brunner-Munzel’s test.