Dear Dr Turkheimer,
>I will try to qualify better the previous statement.
>In the case of Katya the following should hold.
>
>a)Having any prior information on the localization of the signal obviously
>disqualifies the whole brain correction because the set of p-values is not
>homogeneous any more.
Agreed, whole-brain correction is inappropriate here (although I
wouldn't put it quite as strongly as you do - whole-brain corrected
statistics do still have a precise meaning).
>In principle one should then apply the correction to the restricted
>homogeneous set,e.g. the region. However, and here is the conundrum, we
>should specify what we mean by prior information.
Absolutely, and not just in principle, but also in practice. This
what small-volume correction has been set up to do. Conceptually
it's not really that much of a conundrum. The null hypothesis is
simply no true difference between conditions (or whatever) in this
small group of resels. The p value reflects the probability, under
this null hypothesis, of seeing activity at least as great as is
actually observed within this small volume. Because of the nature of
the hypothesis, activity in voxels outside the small volume becomes
irrelevant (leaving aside spread of signal from smoothing).
You don't have to ASSUME any prior information at all. You could
have plucked your region of interest out of the air, purely on the
basis of whim, or some prior prejudice. You could still set up a
clear, regionally-restricted hypothesis, a priori, and this is all
that is required.
Incidentally, we're still in the realm of classical statistics in
SPM99, so we don't have recourse to building in prior information in
the sense of prior and posterior probabilities (although I believe a
Bayesian approach is under development!).
>b)It is evident that Katia has seen a cluster under threshold in the PFC
>that she believes more significant than others. She probably has some
>evidence that distinguishes that cluster from different clusters within the
>PFC. What Katia knows about the PFC probably implies the partition of the
>p-values in the PFC in a number of subsets of homogeneous p-values. A
>consistent approach should formalize Katia belief into a set of smaller
>regions (probably many) within which the correction should be applied. Good
>luck to her statistician.
I believe that there is a simpler approach, as above. Perhaps she'll
be able to leave her statistician in peace after all.
>c)Richard Perry mentioned a case where the region was selected because
>activated in a previous study. Here I do not think the correction should be
>applied at all because there is no global null hypothesis to disprove.
Sure, there is no global null hypothesis at all. The null hypothesis
is now set up purely in terms of the resels within the small volume.
So although whole-brain correction is not appropriate, small-volume
correction is still sensible. The only alternative is to make your
null hypothesis about one single voxel (avoiding the multiple
comparisons problem altogether). This is what we used to do before
SVC became so straightforward. But ones anatomical hypothesis may
not be sufficiently precise to make this realistic.
>Scientiic inferences (not probabilistic) should be based on a comparison of
>the two patterns, effetc size, anatomical considerations, circumstantial
>information etc.
Sorry, I didn't quite get the point here.
Best wishes,
Richard.
--
from: Dr Richard Perry,
Clinical Lecturer, Wellcome Department of Cognitive Neurology,
Institute of Neurology, Darwin Building, University College London,
Gower Street, London WC1E 6BT.
Tel: 0207 679 2187; e mail: [log in to unmask]
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