Look, what you've written above is based on misunderstanding how an F-test works. I've already explained repeatedly why what you're saying here, which is the same thing you've said each time before, is not correct.

This study contains a failure of an F-test. Because of how the F-test is structured, failure of an F-test to prove forall X P(X), is not inductive evidence, nor evidence of any kind at all, that P(X) is false for most X.

I will try to be more polite, but you need to a) read the study, and b) learn how an F-test works, before you can talk about this. But I just don't understand why you keep making confident assertions about a study you haven't read, using a test you don't understand.

The F-test is especially tricky, because you know you're going to find some difference between the groups. What difference D would you expect to find if there is in fact no effect? That's a really hard question, and the F-test dodges it by using the arbitrary but standard 95% confidence interval to pick a higher threshold, F. Results between D and F would still support the hypothesis that there is an effect, while results below D would be evidence against that hypothesis. Not knowing what D is, we can't say whether failure of an F-test is evidence for or against a hypothesis.