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I had started writing this message last night prior to receiving Andrew's 
timely response, but here is just a little perspective on this discussion. 

Indeed, the technique of squaring and summing the individual z-values and 
comparing the result against the Chi-squared distribution should not be 
considered as a substitute for performing a proper group analysis.  Between 
subject variation is not modeled with this approach and generalization to 
the population level is severely limited.  However, measures such as this 
are not without precedent.  Techniques for the meta-analysis of a 
scientific literature routinely employ such approaches since the z-score 
and related measures can be taken as a measure of statistical effect size. 
Increasingly, more and more meta-analytic assessments of results in the 
functional imaging literature are being reported as part of newer research 
articles and as parts of quantitative literature reviews.  Noteworthy is 
the Brainmap database which attempts to record activation results from the 
literature for contrast and comparison.

For the consolidation of the results of individual subject results these 
values may have an insightful, if somewhat constrained interpretation. 
 Depending upon the statement about the data that the person is trying to 
make it is possible to make some crude statements about their individual 
z-score maps. As was mentioned, if the z-scores are assumed to be i.i.d., 
then a new random variable z may be created by summing the zscores and 
dividing by the square root of the number of values summed.  This would be 
a crude assessment of whether there is a systematic bias in the direction 
of the mean z-value, presumably related to the paradigm in question. 
 However, the assessment of whether or not there is evidence for any sort 
of variation at all amongst the values (e.g. regardless of the sign of the 
test) would be crudely assessed by the squared-summed z-value approach. 
 Again, these are poorman's statistics but can, with caution, appropriately 
assess basic characteristics of the data across individuals.  So, as Andrew 
points out "both are right". The resulting statistical image pattern from 
such techniques should be similar, though not exactly equal, to those given 
from an SPM conjunction analysis, less data masking and the SPM probability 
adjustment.

Arguments over statistics such as this, however, are frustrating for the 
non-statistically minded who simply want to know "which test is better?". 
 Regretably, there are no easy answers if the experimental design is 
ill-defined from the outset and one is hunting for significant findings. 
 The following approach will usually help to make certain that one will 
have available the most appropriate analytical approach to understanding 
their data.  Determine a priori which form of experimental design is most 
suitable for testing your hypothesis, then perform the analysis that is 
most appropriate for your experimental design.  The habit in this field of 
collecting data first and only then deciding how to analyze it is 
undoubtedly going to result in more confusion that fundamental results 
about brain function by filling the literature with post hoc statistics 
making meta-analytic assessment of findings useless, if not impossible.

I am certain that discussion on this issue will continue.

Sincerely yours,

Jack

********************************
John Darrell Van Horn, Ph.D.
Laboratory of Brain and Cognition, NIMH
National Institutes of Health
9000 Rockville Pike
Bethesda, Maryland 20892

Phone:	(301) 435-4938
Fax:	(301) 402-0921
email:	[log in to unmask]




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