As I?d showed by simulation the test statistics p-values are uniformly distributed only when the respective null hypotheses is EXACTLY TRUE. By other words, it is not ENOUGH at all the no-rejection decision to assure uniform p-values: if we not hit the *bull?s eye* they tend strongly to be smaller than for true H0, therefore one does find *anomalous* higher proportion of the p< alpha condition. ****** By other hand the usual *technical jargon* there is no difference (on means, on variations, on correlation coefficients, etc.) is advisable to be banned for didactic/teaching purposes, exactly because it fatally suggests (wrongly) that one can ever to state equality by means of significance tests. This interpretive error I was able to found here.