From the abstract:

One of the most basic topics in many introductory statistical methods texts is inference for a population mean. The primary tool for confidence intervals and tests is the Student t sampling distribution. Although the derivation requires independent identically distributed normal random variables with constant variance, most authors reassure the readers about some robustness to the normality and constant variance assumptions. Some point out that if one is concerned about assumptions, one may statistically test these prior to reliance on the Student t. Most software packages provide optional test results for both (a) the Gaussian assumption and (b) homogeneity of variance. Many textbooks advise only informal graphical assessments, such as certain scatterplots for independence, others for constant variance, and normal quantile–quantile plots for the adequacy of the Gaussian model. We concur with this recommendation. As convincing evidence against formal tests of (a), such as the Shapiro–Wilk, we offer a simulation study of the tails of the resulting conditional sampling distributions of the Studentized mean. We analyze the results of systematically screening all samples from normal, uniform, exponential, and Cauchy populations. This pretest does not correct the erroneous significance levels and makes matters worse for the exponential. In practice, we conclude that graphical diagnostics are better than a formal pretest. Furthermore, rank or permutation methods are recommended for exact validity in the symmetric case.

The abstract highlights a critical evaluation of the efficacy of preliminary testing for normality, suggesting it might be counterproductive.

Your objective is to replicate the simulation study conducted by Schucany and Ng using R. As a deliverable, a comprehensive report created in RMarkdown is expected, inclusive of relevant tables, plots, and a detailed summary of your findings. While adherence to the presentation style of the original paper is encouraged, you are also free to explore alternative methods of data visualization or summarization. Additionally, you are welcome to extend the scope of your investigation by incorporating other scenarios in your study (e.g., applying different distributions in the main analysis).