On Tue, 5 Apr 2005, Bjorn Roche wrote:
> On Thu, 31 Mar 2005, Thomas E. Nichols wrote:
>
> <snip>
>
>> If you would like to conclude that the effects corresponding to
>> all three of these contrasts are simeltaneously "real", then you
>> want to use the "Conj'" null.
>>
>
> <snip>
>
>> For more, see http://www.sph.umich.edu/~nichols/Conj and the
>> two articles on Conjunctions on the "In Press" section of
>> NeuroImage website.
>
> Tom,
>
> Thanks again for your previous reply. I have taken a look at your
> paper and installed your patches to SPM 99. I assume the patches change the
> meaning of "conjunction" in the spm gui so that conjunction is now MS/CN from
> you paper and "global" is now MS/GN. I understood from your paper that the
> correct conjoined region is found by taking the intersection of all voxels
> which tested significant in the individual tests (eg performing a voxel-wise
> logical AND).
>
> If that is the case, I should be able to get the same region by
> running the tests individually and finding the intersection os those regions.
> Using the marsbar package, I was able to do precisely that for the FWE
> correction, but not when I used the FDR corrections. Is it invalid to use FDR
> corrections with conjunction?
I have taken a closer look at the Friston et al. paper
("Conjunction Revisited") and I think that this partially answers the
question, so thank you again, Tom, for pointing that out.
I see that the MS/CN method is conservative, so Friston et al
suggest that there is an exact way: to use "small-volume adjusted P values
centered on the maximum of the first contrast... [this approach] is exact
but requires you to specify an order in which the contrasts enter the
conjunction."
So, the question I have now is: why can't we simply find the
intersection of significant voxels, (eg voxels that are significant in
each contrast)? This simple method, which does not require us to choose an
order, seems to satisfy the problem: as stated by Friston et al, "If the
objective is to infer a conjunction of effects, then it should be
sufficient to test each contrast separately and establish they are all
significant."
I would conclude that if we have a set of voxels that are
significant in each contrast, then we have a significant conjunction
effect, if not, we don't. The only disadvantage I can see with this
approach is that we don't get the usual set of statistics, t, Z-score,
etc. (Although I admit I am also unclear at this point what meanings these
statics would have in any conjunction. If they are simply the "least
convincing" of the bunch, then that can be produced by the intersection
method I just described.)
Okay, thanks for the feedback!
bjorn
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