Set up Normal distribution Type I error Power Right skewed continuous – lognormal What the parameterizations look like Type I error Power This 1990-wants-you-back doodle explores the effects of a Normality Filter – using a Shapiro-Wilk (SW) test as a decision rule for using either a t-test or some alternative such as a 1) non-parametric Mann-Whitney-Wilcoxon (MWW) test, or 2) a t-test on the log-transformed response.
Update to the earlier post, which was written in response to my own thinking about how to teach stastics to experimental biologists working in fields that are dominated by hypothesis testing instead of estimation. That is, should these researchers learn GLMs or is a t-test on raw or log-transformed data on something like count data good enough – or even superior? My post was written without the benefit of either [Ives](Ives, Anthony R.
This post has been updated. A skeleton simulation of different strategies for NHST for count data if all we care about is a p-value, as in bench biology where p-values are used to simply give one confidence that something didn’t go terribly wrong (similar to doing experiments in triplicate – it’s not the effect size that matters only “we have experimental evidence of a replicable effect”). tl;dr - At least for Type I error at small \(n\), log(response) and Wilcoxan have the best performance over the simulation space.