Dear Jack,
Thanks for your note. Just to consolidate the (3) levels at which
activation effects are characterized within SPM we have:
Given the linear model
Y = X*B = e
(i) The fitted repsonse (X*B) or parameter estimates (B) which
have hitherto been referred to as effect size (I think, in light of
your comments, I will remove the label 'effect size' from SPM99 and just
put 'responses').
(ii) The statistic upon which inference is based. I.e. T = B/se(B)
where se(.) is standard error. This statistic is Gaussianized to give
Z for tabular reporting so that p(z > Z) = p(t > T) = p.
(iii) The associated p values (p) corrected and uncorrected for the
volume.
Although the Z variate is a statistic that discounts degrees of freedom
etc. I do not think it is an effect size in any formal sense. Clearly
none of these levels constitute an 'effect size' proper and there is
scope for additional characterizations along these lines. Some
interesting ideas, related to confidence intervals for an activation,
have been discussed and someone else may wish to comment here. Another
interesting approach is the use of mixture models that facilitate a
Bayesian-like inference about the posterior probability of activation.
With very best wishes - Karl
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Dear Karl,
Thank you very much for helping to clear up confusion with regard to what
effect sizes are being plotted in SPM and in several of your group's
research articles. I just needed to be sure I wasn't missing something in
how this was being presented.
Also, thanks for your comments with regard to my questions about how best
to understand and report effect size estimates. Eric Zarahn brings up
several additional points that are very relevant to this whole issue and
probably have not been fully appreciated. Another might be the small
subject sample sizes in many studies. Considering the recent interest in
population-level generalization of neuroimaging results, how statistical
effect sizes are represented and how these other issues contribute to
effect size take on an increased importance. Again, I look forward to
hearing what others have to say about these issues.
Warmest regards,
Jack
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