Dear Karl,

I have a couple of questions about how statistical effect size is being 
represented in SPM as well as in several recent articles from your group. 
 Perhaps you can clarify this for me and also address a larger issue 
related to the reporting of statistical effect size.

In your recent manuscript ("Multi-subject fMRI studies and conjunction 
analyses") Figures 3 and 4 have Y-axes labels indicating "Effect Size" but 
it is unclear what this measure of effect is with respect to.  Are these 
values given in percent change relative to whole brain mean or the specific 
voxel mean?  Additionally, in your email to Dr. Muftuler, you indicate that 
in the paper "Detecting activations in PET and fMRI: Levels of inference 
and power", Neuroimage 40, 223-235 (1996) that the 'component score scale' 
estimates are completely independent of the inference (that is the test 
statisitic or p value) and that if the global normalization was to a grand 
mean of 100 then the scale is simply percent signal change relative to the 
whole brain mean signal.  So then are these two things actually the same 
thing - just named differently?  How do these values relate to other 
measures of effect size that have been reported such as in Buchel et al. 
(Science, 283, pp. 1538-1541, Figure 2)?  Is this again another name for 
the same thing?

In a more philosophical vein, can percent change indices really be 
considered measures of effect size in the traditional sense?  For instance, 
classical effect size estimates are indeed 'adimensional', based upon the 
inferential test statistic used to evaluate the statistical model, take 
into account measurement variance, and are independent of the study sample 
size.  They are typically taken to be population level estimates and 
include such measures as Cohen's d statistic (for evaluating t-tests), 
eta-squared (for ANOVA, etc), among others.  These measures are often used 
to make estimates of the number of subjects needed to reliably obtain a 
statistically significant experimental result.  Additionally, statistical 
test values may be culled from research articles in the literature, 
converted to effect size estimates, and assessed under meta-analysis, or as 
been more recently discussed and demonstrated, pooled across individual 
subjects in an fMRI investigation to provide evidence for consistency of 
activation over a subject sample (e.g. sum(Z)/sqrt(N), Chi-square, or your 
conjunction analysis approach).  However, the percent change measure is not 
a standardized difference with respect to the variation in the measurement 
but is  difference taken as a ratio to the whole brain mean or the mean of 
some other stimulus condition.  Since the  method for computation of 
percent change appears to vary between reports in the literature as well as 
experimental designs, are there any troublesome distributional properties 
to worry about that might express themselves if this measure is looked at 
in meta-analysis?  Are there any advantages to reporting effect sizes like 
the classical measures mentioned above in order to facilite better 
comparison between studies, permit better estimates of statistical power, 
as well as enable evaluation of the overall body of research? Could you 
comment on this?

I appreciate your clarifying these issues and perhaps there are others on 
the list can provide some additional thoughts on the broader topic how to 
best report statistical effect size from neuroimaging studies.

Warmest regards,

Jack Van Horn


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John Darrell Van Horn, Ph.D.
Laboratory of Brain and Cognition, NIMH
National Institutes of Health
Building 10 Room 4C104
9000 Rockville Pike
Bethesda, Maryland 20892 USA
Phone: (301) 435-4938
Fax:     (301) 402-0921
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