Earlier quoted context omitted.
> The t-test is extremely robust to departures from normality given equal sample sizes That's over selling it. Its very sensitive to fat tails and skew. That's the reason robust testing and estimation is a thing. Wilcox's research would be a good near contemporary place to start [0][1]. [0] Wilcox, Robustness of Standard Tests https://onlinelibrary.wiley.com/doi/abs/10.1002/978111844511... (paywalled) Abstract: Conve…
> Its very sensitive to fat tails and skew. That's the reason robust testing and estimation is a thing. Yeah, I shouldn't have said "extremely". Its much more robust than is commonly perceived, but that does not make it "extremely" robust. Thank you for the correction. But please note that I specified equal sample sizes , so the fact that "there are general conditions under which these methods can provide poor contro…
In the book Wilcox champions robust estimators and tests (a la Huber, Tukey) because efficiency of MLE is very brittle.