From observational data to a designed experiment: a complete applied-statistics workflow with the Palmer penguins

Statistics courses often teach confidence intervals, t-tests, analysis of variance (ANOVA) and experimental design as separate topics, so students rarely see how one decision leads to the next, or why observational data cannot answer a causal question. This case study follows a single question through a graduate course project: do Palmer penguins differ in body mass by species and sex? The project moves through exploration, confidence intervals, a Welch t-test, one-way ANOVA with assumption checks and robust alternatives, Tukey comparisons and effect sizes, a two-way model with an interaction, a blocked analysis, and the design of a randomised 2³ factorial experiment. The results reproduce known differences, so the value lies in the decisions: where the data ruled a method out, what to do when an assumption fails, and why a block that explains nothing still teaches something. The R script and the data accompany this preprint. Status: preprint, not peer reviewed. Submitted to Teaching Statistics (Wiley) on 25 October 2026. Files: the article (PDF); final_project.R, the whole analysis as one R script, in the order of the article (MIT licence); penguins.csv, the Palmer penguins data from the palmerpenguins R package (Horst, Hill & Gorman, 2020; CC0); a README and the licence file. Use of generative AI: the article's text was drafted with Claude (Anthropic; Claude Opus 5.5) from the author's analysis outputs. The author ran every analysis, reviewed and revised the text, and takes full responsibility for the content (see Section 2 of the article).