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

From the abstract:

Student’s two-sample t test is generally used for comparing the means of two independent samples, for example, two treatment arms. Under the null hypothesis, the t test assumes that the two samples arise from the same normally distributed population with unknown variance. Adequate control of the Type I error requires that the normality assumption holds, which is often examined by means of a preliminary Shapiro-Wilk test. The following two-stage procedure is widely accepted: If the preliminary test for normality is not significant, the t test is used; if the preliminary test rejects the null hypothesis of normality, a nonparametric test is applied in the main analysis. […]

This procedure seems okay, but there are some serious problems with it. Many researchers believe that by employing this two-stage procedure, we lose control over the Type I error. Is this true? The question is not easy to answer. First, it requires a solid understanding of NHST (Null Hypothesis Significance Testing). Second, there is no way to check this except through Monte Carlo simulations. This problem has been extensively discussed in the statistical literature, but to this day, many simulation studies are published.

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.