A while ago I posted a question regarding performing post-hoc power analyses in meta-analyses and was given a couple of useful links to discussions regarding why this isn’t a good idea. From my reading of these discussions, and the suggested academic articles, one should rather than trying to do a post-hoc power analysis look at the confidence interval of the effect size of a null result to discern whether it contains an effect size that one would deem as relevant.
This is all well and good when having just a single effect size that isn’t significantly refuting the null hypothesis. However, how should one approach power indicators for omnibus tests of several effect sizes? For example, I might want to do a moderator analysis with two or more levels of a moderator, yielding an estimate and confidence interval for each moderator level. How can I in this case talk about the sensitivity of my test?