Sometimes researchers (especially in collaborations) have two opposite but sound theories: There is a difference between two groups or there is only negligible difference. Now they ask their statistician. How should he approach the situation?
If he does a point hypothesis test, he favours the difference party since only their theory can be confirmed in case of rejected point hypothesis whereas not rejecting the point hypothesis teaches nothing.
If he does only equivalence testing, he favours the negligible difference party for the analogous reason.
Should he do both, of course with multiplicity correction? So a TOST for equivalence and a point hypothesis test? Or a TOST and a respective relevance test?
This procedure would have three outcomes:
- Equivalence of both parameters up to negligible differences.
- Large enough differences.
- Nothing to learn since both hypotheses have not been rejected.
Is such an "et-et"-approach reasonable? Why do we hardly see such "et-et"-analyses in publications? This is a general question for reasoning. So multiple answers are encouraged and I do not restrict this question to particular models.