Earlier quoted context omitted.
Not OP, but [0]: > If the data do not contradict the null hypothesis, then only a weak conclusion can be made: namely, that the observed data set provides no strong evidence against the null hypothesis. In this case, because the null hypothesis could be true or false, in some contexts this is interpreted as meaning that the data give insufficient evidence to make any conclusion; in other contexts it is interpreted as…
Ah thanks, I understand this aspect. As I say, they simply failed to rejected the null hypothesis, and their approach here seems perfectly valid. The authors did overreach in their interpretation of the result. But OP said ANOVA is wrong, and that the alpha value is wrong. I don't understand how they can say this without understanding this domain, the intervention, and knowing what effect size could be expected. Mayb…
I said that failing to show a statistically significant difference is not the same as showing equivalence with statistical significance. Tests designed for the former cannot do the latter with any amount of data. You need a different test for that, or at least the same underlying statistical test used in a different manner. Can you explain what about this implies that "ANOVA and the alpha value are wrong?"
I'll confess to having never really learned ANOVA, but it sounds like it's a family of models generalizing the t-test. You can indeed perform equivalence and non-inferiority testing with the t-test, as I did in my OOPSLA 2018 paper. You just have to use it in a different way than it sounds like they did here.