Dear Rob,
> I'm trying to understand the situation with probability thresholds
> in a conjunction analysis where you are trying to find activation
> that is common to both contrasts (i.e. areas which are significant
> in both contrast A and contrast B).
>
> As I understand it you can't just use the square root of the desired
> voxel-wise p value on the individual contrasts, because the logic
> that if the p value of contrasts A and B is SQRT(X), the p value of
> the conjunction of A&B = SQRT(X) x SQRT(X) = X is incorrect,
> because the X here would relate to the probability of either one
> being non-significant, not both of them (which is what is required
> for the null hypothesis in a conjunction analysis).
Correct.
>
> The suggested method to doing a conjunction appears therfore to be
> to threshold you individual contrasts at the original p value (X)
> and then just run the conjunction on these contrasts. However this
> seems to be to be a very conservative test, with potential for
> sizeable amount of false negatives. Is there a compromise method
> that falls between these two solutions?
I don't think there is a principally correct one. If you think about
what you are doing with a conjunction you are actually asking a much
"harder" question of your data. You are asking, is there an activation
in contrast A AND in contrast B AND contrast C etc. So it is not
really surprising that it makes harder demands on your data, i.e. is
being more conservative.
Good luck Jesper
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