Roberto,
> Thank you for your answer. The one-voxel situation is an extreme
> case: one could imagine then that the null hypothesis is true in
> only two voxels. A Bonferroni correction for 2 repeated tests would
> then deliver strong FWE control, am I correct? The strong FWE tests
> used in practice model the complete null; this example shows,
> however, that one could go much lower with the threshold and still
> have strong FWE.
There are in fact step-wise tests which try to do this. They
basically apply Bonferroni, if that rejects k tests, you pretend like
you only have v-k tests, and apply it again, and so and and so on.
See this FWE review paper
http://www.sph.umich.edu/~nichols/Docs/NicholsHayasaka.pdf
for more on this. As it turns out these Bonferroni-related methods
don't work so well with imaging data because our signal is so sparse.
BUT, if you had a setting were only 2 tests were null, they could
help.
-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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