A large part of the discussion on problems with hypothesis testing, p-values etc. focuses on the misuses and misunderstandings for these concepts, most famously that the p-value is the probability that the null hypothesis is true. However, I am wondering about the following: does someone know of a real-live example where a NHST was done correctly and without any misunderstandings and misinterpretations, and in the end there were issues anyway? This should not include cases were a null was rejected that later turned out to be true, or vice versa, because the fact that this will on occasion happen is baked into the procedure. I am also not looking for examples where a Bayesian test would have given a better answer, of which I am sure there are many.
Thanks
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Dr. Wolfgang Rolke
Professor
Univ of Puerto Rico RUM
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