Equivalence Testing versus ANOVA

AttributedPath4 — Fri, 09 Jun 2023 00:58:37 GMT

Hi everyone,

I am working on a paper and would like to include some statistical data. I ran equivalence tests and ANOVA tests but I just wanted to confirm that the statements I am making about the "practical equivalence" of my data are correct.

To find an "essentially zero" value I looked in the literature and found three different sources that would give me a defensible way to calculate this value. For each input, I get that the responses (slopes) are ALL "not practically equivalent".

Yet, when I run ANOVA and a t-test I get that two slopes are significantly different from each other and the other slopes, yet the other three slopes are not significantly different.

I know that equivalence tests and ANOVA are testing different things but I find this confusing because I expected it to be the other way around (that the ANOVA would claim significance and the equivalence testing would reveal that in practical applications that are not significantly different.)

Could anyone help me understand this data better?

Thank you! :)

Re: Equivalence Testing versus ANOVA

Mark_Bailey — Tue, 13 Dec 2022 14:49:37 GMT

The hypothesis test for differences does not include a definition of 'how practically different' the estimates must be to reject the null hypothesis that they are the same. The hypothesis test for equivalence depends directly on such a definition.

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Equivalence Testing versus ANOVA

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