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Keith,

> We have significantly corrected p-values (p = 0.05) at both the voxel and
> cluster level for a VBM study.  Now if I understand what I have read
> regarding this topic, the cluster level significance is corrected for
> spatial extent (k) only, whereas the voxel level is corrected for peak
> height (u) only.  Is that correct?

That is correct.

The joint cluster size and peak height (k,u) results only exist for
Gaussian random fields (not t or F fields).



> Regarding reporting cluster-level differences, in a previous post
> (http://www.jiscmail.ac.uk/cgi-bin/wa.exe?A2=ind0103&L=spm&P=R1599
> <http://www.jiscmail.ac.uk/cgi-bin/wa.exe?A2=ind0103&L=spm&P=R1599> ) Tom
> Nichols stated  - "Finally, remember that these results are only valid for
> stationary random fields (the smoothness is W everywhere in the brain).
> This makes the cluster size p-values invalid for VBM."  I am curious to know
> why the smoothness would vary throughout the image and why this invalidates
> its use in VBM?

First, note that the smoothness assumptions are not on the data
itself, but on the component fields.  You could construct the
component fields as follows: Take the data, subtract off the (true)
signal, and then divide by the (true) standard deviation image.  For
VBM, the "signal" is the population mean image.  So we are concerned
not with the smoothness of VBM data itself, but rather the smoothness
of each individual's departure from the group mean.

So the smoothness of VBM data varies because of differing topological
structure across the brain and across subjects.  White matter is
very smooth, while the cortex is convoluted; across subjects,
cortical folds do not line up exactly, while there is much greater
agreement in subcortical structures.

These differences gives rise to differing amounts of smoothness; to
convince yourself of this, just take a look at the RPV.img, an image of
the (estimated) local RESEL density.  If stationarity held, this image
would be uniform.  In the VBM data I've seen th RPV image was very
non-uniform.


As to why stationarity is required for the cluster size p-values, it's
simply as far as the theory as gotten.  There is work afoot by myself
and Keith Worsley (and others?) to relax this assumption.


-Tom