> but when a study size is small and you still find a difference, then it implies the effect size is large That’s only true if it holds across multiple studies

> but when a study size is small and you still find a difference, then it implies the effect size is large That’s only true if it holds across multiple studies. Otherwise it might simply be random variability. By your argument, a study with n=4 that showed an effect would imply a huge effect size. No. It implies that the measured signal is highly variable, and that you got lucky on 1:3 odds. Check out regression towards the mean [1]. (Note that if you’ve got a good underlying model of the variability, n=4 can work. In fact, it’s routinely done in specific applications, such as transcriptomics. But even there it’s far from ideal, and it’s supported by a stringent error model.) [1] https://en.wikipedia.org/wiki/Regression_toward_the_mean https://en.wikipedia.org/wiki/Regression_toward_the_mean