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.

Your goal is to replicate a simulation study done by Weber and Sawilowski using R. As a deliverable, I expect a report written using RMarkdown, including appropriate tables, plots, and a summary of the results. In terms of presentation, you may follow the original paper, but feel free to experiment if you want to plot or summarize the data differently. If you wish to include other scenarios (e.g., use other distributions in the main part of the study), feel free to do so.