Dear George,
Please allow me to suggest an answer to this. I am far from an expert
however so if I am wrong I hope someone will let us all know.
Specifically, I would like to address the combinatorial probability
you mentioned.
If you don't mind I will simplify the example a bit. Imagine I have
three independent contrasts (a,b and c). Hypothetically lets say that
when I test all three at p<0.05
uncorrected I get no significant voxels and that to see my areas I
need to increase the threshold to p<0.06 uncorrected.
I then (inclusively) mask the contrasts to find voxels active at
p<0.06 in all three contrasts. Now I want to make a statement about
the probablility of finding these voxels in all three contrasts. I
know the probability of a AND b AND c is the probability of a
multiplied by the probability of b multiplied by the probability of c.
This gives me a probability of 0.000216. Now in the literature I have
seen (as it seems you have) people report this as the probability of
finding active voxels in contrasts a b and c is 0.000216.
I think that this is incorrect however. I view this value as the
combined probability of making a type 1 error - in other words the
probability that you have falsely rejected the null in contrast a AND
b AND c. If this is the null I am testing then I think the analysis
become a conjunction global, as to reject this null I only need
to reject any single one of those null hypotheses at the original
p<0.06 level.
In that case my p-value doesnt refer to the chance of seeing that
voxel in each contrast, rather the probability of seeing it in at
least one of the contrasts.
Hope this helps (and is correct),
Geoff
On 07/08/07, George SPM <[log in to unmask]> wrote:
> Hi,
> I would like your opinion about an analysis I have done:
> I use a contrast 1, sensitive to psychological parameters A and B (but not
> C) to define a functional ROI. I thresholded this contrast at .01
> uncorrected. I assume that the regions surviving from contrast 1, encode
> only A and B.
> Then I use contrast 2, sensitive to psychological parameters B and C (but
> not A) and I search for voxels surviving WITHIN the abovementioned fROI. I
> find an area surviving at p=.05, corrected this time, and I assume that this
> area encodes B, since C has been excluded by the fROI.
> Is this analysis correct, in the sense that the area actually encodes B
> only? Is this analysis considered corrected? The probability that this area
> will survive is .05x.01=.0005.
> Thanks
> George
>
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