point out validity conditions of corrected p-values #7
Description
email to Remi:
Yes, the problem lies with Eq. 21, which assumes that "the effect is only present in a small area" (p. 386). That's one of the things I'm not really happy about with this method, and which I simply adopted from the underlying work by Friston because I didn't have a better idea. The problem occurs when we look at spatially extended prevalence inference. Say in a single voxel / searchlight we'd like to reject the H0: prevalence <= 0.5 (the majority H0). How does this generalize to a set of voxels / searchlights? Is our spatially extended H0 that prevalence is smaller than but possibly close to 0.5 everywhere? Or is our spatially extended H0 that prevalence is 0 almost everywhere and possibly close to 0.5 only in one or a few regions? The multiple corrections problem is quite different in the two cases. For me the thing that decided it was that as far as I can see, there is no way to use permutations to implement the former, so I implemented the latter. ... Anyway, the whole thing breaks down if you only test in one or a few voxels / searchlights / ROIs, and I should probably explicitly write in the documentation under which circumstances the corrected p-values make sense at all. Thanks for making me aware of that!