Dear Feng,
Some minor clarifications:
> FWEc corresponds to FWE corrected at cluster level and this option needs an initial height threshold [..]
This is correct. Just as a note, when going with FWE (or FDR) on cluster level you wouldn't use a corrected voxel threshold for initial thresholding, as this would mean to control for multiple testing twice.
> Regardless of I whether or not changing the default value of the option defaults.stats.topoFDR
Changing that option results in a loss of the cluster-level qFDR-corr listed in the results table, no idea whether it affects the FDRp or FDRc.
> Let r be largest i such that p(i) <= (i/V) * q
As a note, in the methods paper by Genovese et al. (2002) it's p(i) <= i/V * q/c, where c is a constant term reflecting the distribution of p values across voxels. They propose two different c, either c being the hamonic series 1/1 + 1/1+1 + ... 1/V, which holds for any distribution of p values, or c = 1, which was chosen for spm_P_FDR and holds for independent p values and positive dependence, with the latter being defined as Gaussian distributed noise with with nonnegative correlation across voxels. This seems to be a reasonable approximation for fMRI according to them, but it's nonetheless interesting that they didn't implement the conservative c ;-)
> In short, I used initial height threshold first to obtain FDRp value at left bottom
> and then used the FDRp value as height threshold to see the whether there are survived voxels.
Yes. For whole-brain analysis you go with an uncorrected height threshold, which can be based on a p or T value. You look at the bottom of the table. You threshold the data a 2nd time with an uncorrected height threshold, but this time enter the FDRp value.
> different initial threshold corresponds to different FDRp values (T values), but they all
> finish the Topological FDR p<0.05 corrected at height level. Is this right?
Yes. The .05 is hard-coded to reflect the usual alpha .05. Go with a certain initial height threshold, and SPM tells you which T value to chose to have a topological FDR of .05.
> If so, if I used this method, how should I describe/write in my paper?
You have to report the initial voxel threshold, be it a p or T value, you have to report the FDR (well, .05), you should make sure that it was applied on peak level (if you do so), and possibly, you might want to report that this FDR resulted in a T threshold of xyz. When looking at papers it is often very difficult to understand how the data was thresholded. This is especially problematic with FDR, as there are two types of topological FDR plus the old voxel-FDR. Something like "data was thresholded based on a false discovery rate of p < .05" is useless, was it the old voxel-FDR, was it topological, if so, on cluster or peak level, and which initial threshold was chosen? And the initial threshold is also relevant, thus "data was thresholded with a topological peak FDR of p < 0.05" is also insufficient.
For the other issues about FDR p values, have to look at the PDFs more closely.
Best,
Helmut
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