I need help in deciding which responce function to use in (post-hoc) power calculation for Mann-Whitney test: normal, laplace, logistic etc. Is there any theoretical resource that could explain in which case which fonction is most appropriate? Thank you in advance!
I would typically use ordinal. The Mann-Whitney test is a rank-based test, so the results are invariant under monotonic transformations. If you have some idea of the underlying distribution, then you could choose that. However, ordinal will always work.
There is a huge literature on why one should NOT do post hoc power analysis. That doesn't keep my clients from asking for it.
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