Paper PDF: download it from the additional files on this page.

From the abstract:

The nonparametric Wilcoxon Rank Sum (also known as the Mann-Whitney U) and the permutation t-tests are robust with respect to Type I error for departures from population normality, and both are powerful alternatives to the independent samples Student’s t-test for detecting shift in location. The question remains regarding their comparative statistical power for small samples, particularly for non-normal distributions. Monte Carlo simulations indicated the rank-based Wilcoxon test was found to be more powerful than both the t and the permutation t-tests.

The problem of comparing two samples seems to be “solved,” but there are still many debates about the appropriate statistical procedures. The standard method is to use the two-sample t-test, but, as you probably know, it can only be used if it is reasonable to assume that the observations came from a normal distribution. So-called non-parametric alternatives have been proposed that do not make these assumptions. The “classic” non-parametric test for two samples is the Mann-Whitney U test, and the more sophisticated one is the permutation t-test, which relies on resampling techniques to approximate the sampling distribution of the test statistic.

Suggested final-project direction: replicate (and optionally extend) the simulation study using R.

Deliverable (suggested): a fully reproducible report written in Quarto (.qmd) with tables/plots and a clear summary of your findings, aligned with the final project requirements.