Robyn & Russ,
> the Gaussian random field corrections require assumptions regarding the
> smoothnes of the residuals, which would certainly not be true for
> unsmoothed trace or FA images, and I doubt that you want to smooth
> these images.
There are two issues here, Normality and smoothness of residual images.
Normality is needed for any statistical test used in SPM; I haven't
looked at FA images, but if they are not close to zero and they don't
have problems with outliers, then I would bet that Normality won't be
a problem.
Smoothness is needed for the random field theory (RFT) corrected
inferences to be valid; from some simluations we've been doing
recently, for t images with moderate df (~20), you need at least 3
voxel FWHM or the RFT results will be conservative.
For the RFT cluster size test the smoothness is also assumed to be
uniform, that is, the error images are assumed to have a stationary
covariance structure. If they're not stationary, you'll get greater
than expected false positives in smooth areas and reduced power in
rough areas. Again, I haven't looked at FA images to know if this is
reasonable, but you can get a sense by looking at the RPV images,
images of roughness.
> It may be possible to use the false discovery rate
> correction, but I'm not sure whether the non-normality of the FA images
> would be a problem.
The False Discovery Rate, first off, assumes that your uncorrected
voxel-level p-values are valid; this requires that Normality hold.
The other FDR assumption is positive dependency where the
null hypothesis is true, that is, positive spatial correlation of the
null-regions of the statistic image. Again, I haven't looked at this
for FA images; for fMRI images this seems to be reasonable.
RE: SnPM. If you have independent data, as in FA images from a cohort
of subjects, then SnPM is one way to avoid parametric assumptions.
( http://www.fil.ion.ucl.ac.uk/spm/ext#SnPM ) It provides corrected
voxel-level p-values and corrected cluster-level p-values. In low df
or low smoothness settings, SnPM's voxel-level corrected p-values can
be substantially more powerful than the RFT t results (See Nichols &
Holmes, HBM 15:1-25 (2002)). SnPM's cluster-level inference does not
require stationarity to be valid, but severe nonstationarity can
reduced it's sensitivity.
For the voxel-level normality assumptions, and for general exploration
of your modeled data, my grad student and I have created "SPM
Diagnosis", or SPMd, described here
http://www.sph.umich.edu/~nichols/SPMd
In particular, it creates images of several diagnostic images,
including Shapario-Wilk test of non-Normality, Cook-Weisberg score
test of heterogeneous variance, and Durbin-Watson test of AR(1)
autocorrelation. You can click back and forth between the diagnostic
images and the diagnostic detail (e.g. residual plots, residual
images). It's still a little rough around the edges, but very useable
and useful (I think)!
-Tom
-- Thomas Nichols -------------------- Department of Biostatistics
http://www.sph.umich.edu/~nichols University of Michigan
[log in to unmask] 1420 Washington Heights
-------------------------------------- Ann Arbor, MI 48109-2029
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