Tom,
Thanks a lot for your answer. It really clarifies things.
> > 3) We, in my lab, have both sign permutation and bootstrap
> > implementations of RFX analysis. In our experience, the Bootstrap is
> > always (slightly or a lot) more conservative than sign permutations. But
> > that's an empirical observation...
>
> Interesting. But does this observation apply to univariate (uncorrected)
> P-values, or FWE-corrected (max-based) P-values?
Sorry for not mentioning this point. It applies to both! I couldn't tell in
which situation the difference between Bootstrap and Permutation is the
stronger. Further investigation is still needed, and anyway I'm not claiming
that our observations generalize to all fMRI datasets (I hope not, by the
way).
Yet I'm not surprised by this trend, as I think the Bootstrap somehow relaxes
the population symmetry assumption underlying sign permutations. When
switching from sign permutations to bootstrapping, we sort of exchange an
assumption (symmetry) with an approximation (setting the pdf of the data to
its empirical estimate). So I tend to regard the Bootstrap as "approximately
assumption-free". Having less assumptions, we naturally expect more
conservative P-values.
That would be my explanation, but I am very curious to know your opinion on
this.
Cheers,
Alexis
--
Alexis Roche, PhD
CEA, SHFJ - Orsay, France
Tel: +33 1 69 86 77 73
Fax: +33 1 69 86 77 86
http://www.madic.org/people/roche/
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