Dear AFNI mathematical minds,

To calculate groupwise maps of individual subjects, our lab has used in our publications a meta-analytic formula that essentially treats each subject scan as its own experiement. This simple method combines the individual subject t-statistics (from the linear-contrast between event class A and class B) by voxel-wise averaging of the t-statistics across subjects and multiplying this by the square root of the number of subjects/experiments, e.g.

Donaldson et al Neuroimage 13 (1) pp. 129-142 (2001)

While straightforward and easy to accomplish in AFNI using 3dmerge and applying the -1mult operator, the resultant group maps may not incorporate the random effects of different humans going into the scanner. Moreover, when displaying/presenting group-wise activation statistical maps (i.e. a combined map of patient group X and a combined map of patient group Y), it necessitates having the same number of subjects in each group. In one recent pub, we presented data from two groups, each with 12 subjects.

To directly compare groups, I recently used 3danova on the beta weights of the same linear contrast, directly comparing the same 12 vs 12 subjects. My script (below) included the -mean operator in the anova:

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# using 3dANOVA on Rew vs Neu anticipation group differences: 20c $1 $5

if ( -e rvnANOVA+tlrc.BRIK ) then
rm -rf rvnANOVA+tlrc.*
endif

3dANOVA -levels 2 \
-dset 1 ../controls/as121402/ttestgltreg+tlrc'[96]' \
-dset 1 ../controls/ps012203/ttestgltreg+tlrc'[96]' \
-dset 1 ../controls/ac042902/ttestgltreg+tlrc'[96]' \
-dset 1 ../controls/cp061402/ttestgltreg+tlrc'[96]' \
-dset 1 ../controls/sc053102/ttestgltreg+tlrc'[96]' \
-dset 1 ../controls/sl072602/ttestgltreg+tlrc'[96]' \
-dset 1 ../controls/dn091102/ttestgltreg+tlrc'[96]' \
-dset 1 ../controls/jk040802/ttestgltreg+tlrc'[96]' \
-dset 1 ../controls/mc051702/ttestgltreg+tlrc'[96]' \
-dset 1 ../controls/sr121102/ttestgltreg+tlrc'[96]' \
-dset 1 ../controls/sg061402/ttestgltreg+tlrc'[96]' \
-dset 1 ../controls/gp021203/ttestgltreg+tlrc'[96]' \
-dset 2 ../cr083101/ttestgltreg+tlrc'[96]' \
-dset 2 ../la081001/ttestgltreg+tlrc'[96]' \
-dset 2 ../sw020802/ttestgltreg+tlrc'[96]' \
-dset 2 ../ks082802/ttestgltreg+tlrc'[96]' \
-dset 2 ../jg091002/ttestgltreg+tlrc'[96]' \
-dset 2 ../jb062802/ttestgltreg+tlrc'[96]' \
-dset 2 ../mw082802/ttestgltreg+tlrc'[96]' \
-dset 2 ../mrm071202/ttestgltreg+tlrc'[96]' \
-dset 2 ../mn051302/ttestgltreg+tlrc'[96]' \
-dset 2 ../yt042202/ttestgltreg+tlrc'[96]' \
-dset 2 ../vw101901/ttestgltreg+tlrc'[96]' \
-dset 2 ../tc040502/ttestgltreg+tlrc'[96]' \
-ftr Ftest \
-mean 1 adults \
-mean 2 adolesc \
-diff 2 1 adolvadult \
-contr -1 1 adolvadultcont \
-bucket rvnANOVA

********
The resulting bucket dataset included a subbrik containing a t-test map of the mean of each of the two groups. The stat map generated for each of -dset 1 and -dset 2 looked strikingly like the group-wise activation map generated with the meta-analytic formula, and showed similar t values at most of the significant voxels.

QUESTION 1:

Could I use this t-test map of the ANOVA mean as a valid groupwise map? (In Bob's terms, would this be "reasonable"?). This map basically tells the same story as the meta-analytic formula-derived group map, but may be superior in that it incorporates random effects. Is this correct?

QUESTION 2:

Could I present the anova-mean map of each group seperately (here adolescents and adults) to illustrate each group's distinct combined activation if the two groups did not have equal numbers of subjects, and still have a fair comparison? Alternatively, would the anova-mean map of the group with more subjects be biased toward a stronger voxel t-statistics by virtue of larger sample size and not an authentic group-wise difference in activation?

Please advise. Coming up with kosher ways of deriving group-wise maps that incorporate random effects is always helpful.

Jim B