In Fisher (1955) [from “the triad”]: “it is a fallacy, so well known as to be a standard example, to conclude from a test of significance that the null hypothesis thereby established; at most it may be said to be confirmed or strengthened.”
I just noticed the last part of this sentence, which I think I’ve missed in a zillion readings, or else it didn’t seem very important. People erroneously think Fisherian tests can infer nothing from non-significant results, but I hadn’t remembered that Fisher himself made it blatant–even while he is busy yelling at N-P for introducing the Type 2 error! Neyman and Pearson use power-analytic reasoning to determine how well the null is “confirmed”. If POW(μ’) is high, then a non-statistically significant result indicates μ≤ μ’.
Click to access bernardo-integrated-objective-bayesian-estimation-and-hypothesis-testing.pdf
Click to access fraser_is-bayes-posterior-just-quick-and-dirty-confidence.pdf