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I have conducted a survey. One sample answered a binary question (answer A or B), once with and once without treatment. Now there does not seem to be a treatment effect as the proportions of answers were very similar.

To show that there is no treatment effect, I plan to do an equivalence test as a one-sided z-test. The problem is that there is no meaningful equivalence bound. Every pick of an equivalence bound would be arbitrary.

So my question is, can I go the other way round? May I calculate the equivalence bound x, for which I barely can reject H0 at alpha=0.05.

So I can finally say: The value for x for which we can reject H0 with alpha=0.05 ist ... Or is this bad scientific practice? In my opinion, it is subjective anyway, how to pick the bound. So isn't it more respectable to just calculate the value x for which anyone can see, ok up from this point we can reject H0. Then anyone can decide for themselves whether they really find this bound to be an uninteresting effect size.

Thank you very much guys!

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  • $\begingroup$ are you aware that you can do a two way chi square/fisher exact test on proportions? $\endgroup$
    – carlo
    May 31 '20 at 18:39
  • $\begingroup$ My advise would be to report the result as it is, maybe adding a confidence interval for the true effect. There is no point in retrospectively swapping hypotheses. $\endgroup$
    – Michael M
    May 31 '20 at 19:49

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