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]
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
|