Dear group and Jack,
I think there are several interesting problems that exist in fMRI
for reporting effect sizes. One is the definition of effect: for example
when using basis functions, should one consider the total variance
explained by the basis set as the effect? Another is the temporal
autocorrelation in fMRI data: noise varies with time scale,
so a direct report of signal:noise would not seem to be apposite. A third
is the hemodynamic response: two experiments testing the same neural
hypothesis with fMRI designs on two different time scales will not be
expected to have the same fMRI effect size even if the neural effects
are equivalent. A fourth is the variety of design matrices:
changing the identity of the design matrix could change the variance
of a given parameter estimate, thus changing the reported effect size.
Thanks Jack, for bringing up a great issue to the group. I look
forward to reading what people have to say.
> 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
> 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
> email: [log in to unmask]