Anderson,
> I'm implementing the FDR procedure for studying purposes, and I've
> verified that using c(V)=sum(1/(1:V)) (Benjamini and Yekutieli,
> 2001) is quite conservative if compared with c(V)=1. I'm in doubt
> about which I one should use when the data are smoothed and when
> they are not.
c(V)=1 is appropriate whenever the data are independent or only
positively dependent. Actually, the condition is even weaker: The
independence/positive dependence only need hold on those voxels where
the null hypothesis is true. This seems like a reasonable assumption
for imaging data.
The alternate value of c(V) is only needed when you can't trust the
positive dependence assumption. It is a very severe correction,
though, and in practice, it seems that you need quite pathological
negative dependence to 'break' FDR with c(V)=1.
If you are really worried about the positive dependence assumption,
take a look at the FDR resampling method (Yekutieli & Benjamini, 1999,
J Stat. Plan. & Inference, 82:171-196; Logan & Rowe, 2004, Neuroimage,
22:95-108) which makes no such assumption but should be more sensitive
than c(V) ~ log(V).
-Tom
-- Thomas Nichols -------------------- Department of Biostatistics
http://www.sph.umich.edu/~nichols University of Michigan
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-------------------------------------- Ann Arbor, MI 48109-2029
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