Chapter 6, Exercise 6.4 Make a less extreme example of correlated test statistics than the data duplication at the end of Section 6.5. Simulate data with true null hypotheses only, and let the data morph from having completely independent replicates (columns) to highly correlated as a function of some continuous-valued control parameter. Check type-I error control (e.g., with the p-value histogram) as a function of this control parameter.
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Chapter 6 covers Statistical Testing, including a review of null and alternative hypotheses (and associated distributions), types of error (I and II), as well as challenges and opportunities introduced by multiple testing.
Occam’s razor Heuristic stating that the simplest explanation for a phenomenon is often the best rejection region Subset of possible outcomes for which probabilities under the null hypothesis fall under a low probability threshold, e.