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Matt Hoffman's avatar

I like to mentally find-and-replace phrases like "we cannot reject the null hypothesis" with "man, we can't even reject the null hypothesis", which emphasizes both that rejecting the null is a pretty low bar if you've got a decent sample size and that NHST results are mostly just shorthands.

Unfortunately I have no such trick for making phrases like "the difference was highly significant" palatable, which is of course the real problem.

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Rodrigo C. G. Pena's avatar

I read this post a while ago, but it came back to my mind when I was trying to push ChatGPT's o1 model to derive a relationship between the z-score in null hypothesis testing and a correlation measure. It succeeded in doing so, pointing out to a tradition in statistical behavioral research of relating the point-biserial correlation and the t-test coefficients. You asked for pointers of where the formula you've derived appears in print, but I struggled to find it. Rosenthal and Rosnow 2008 (https://scholarshare.temple.edu/handle/20.500.12613/79) show in equation 2.2 a formula relating t-statistics and the point-biserial correlation that seems to be well known in their community. This formula should approximate yours for large sample sizes

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