Frank E. Harrell Jr, Vanderbilt University - School of Medicine - Nashville TN

The Central Limit Theorem, Testing for Normality, and Other Misleading Ideas

Many statistical concepts and practices are taught in a shallow or mechanistic way, and the full ramifications of such approaches are not appreciated by instructors or students. A case in point is the central limit theorem, which has been used to justify all kinds of statistical approaches even when it doesn't actually work with the sample sizes seen in practice. And statisticians have thought too little about what "work" means. There are hidden assumptions in the CLT that students often do not appreciate. This is related to the nonexistence of nonparametric confidence intervals for population means. Another example is the common practice of testing data for normality, then choosing a parametric test vs. a nonparametric test. This practice involves multiple misunderstandings. The permutation t-test is another example that will be covered.