Posts / Comparing statistical power of the Mann-Whitney U test and the Brunner-Munzel test


In this post, we perform a short numerical simulation to compare the statistical power of the Mann-Whitney U test and the Brunner-Munzel test under normality for various sample sizes and significance levels.

Simulation design

We conduct a simulation according to the following scheme:

Simulation results

Here are the results for some values of $\alpha$ and $n$:

As we can see, in the presented simulations, the Brunner-Munzel test has higher statistical power than the Mann-Whitney U test (especially for small $\alpha$ and small $n$). However, it’s just a single simulation, so we can’t derive a generic conclusion about which test is better. In future posts, I will explore the behavior of these tests in more contexts.