The conventional approach for FMRI group analysis is to take regression coefficients (beta values) and run t-test, AN(C)OVA, or other types of analysis, and ignore the within-subject variability (sampling error of each condition/task/event type). The underlying rationale for such practice is built on the following two assumptions:

(1) Within-subject variability is relatively small compared to between-subjects (group) variability;
(2) Within-subject variability is roughly equal across all subjects.

Current evidences show that up to 40% of variability is usually accounted for with intra-subject variation among all the variability (sum of within- and cross-subject variability) in an activated region of interest. Also there are a lot of variations in within-subject variability across subjects. Violation of either assumption could render a suboptimal or even invalid group analysis, and most of the time it reduces the statistical power at group level. The conventional group analysis method, typically referred to as random/mixed-effects modeling, is mostly a pseudo-random/mixed-effects approach.

Within-subject variability measures how precise/reliable the percent signal change (beta) estimate is from individual subject time series regression model. Since such quantity, contained in the corresponding t-statistic, is conveniently available, there is no reason, except theoretical complexity and computation cost, to waste this piece of information in group analysis.

3dMEMA is developed in R with a mixed-effects meta analysis (MEMA) approach. It effectively takes advantage of estimate precision from each subject, and assigns each subject's contribution in the final result based on weighting instead of equal treatment. More specifically, a more precise beta estimate (meaning higher t-statistic) from a subject will have more say in the group effect; conversely, a less reliable beta estimate (i.e., lower t-statistic) from a subject will be discounted in the MEMA model. Such strategy can be surprisingly tolerant of and robust against some types of outliers compared to the conventional group analysis method.

The primary version of the program is available, and more capabilities are still under development. It currently handles the following model types:

(1) random-effects analysis: one-sample, paired-sample
(2) mixed-effects analysis: two-sample (any analysis with covariate(s) coming soon)

This basically covers whatever you could do with 3dttest before. Noticeably it can't directly deal with sophisticated designs such as ANOVA. F-tests for main effects and interactions provide a concise summary for the factors and their relationship, but eventually most of the time everything boils down to single (not composite) effect testing. In other words, almost all those t-tests in 3dttest/3dANOVAx/3dRegAna/3dLME can be run with 3dMEMA. Hopefully this F-test limitation will change in the future.

You can run 3dMEMA if your analysis can be conceptualized into one of the following types:

A. one condition within one group;
B. two conditions within one group;
C. one condition within two groups with homoskedasticity;
D. one condition within two groups with heteroskedasticity.

As beta precision estimate is important for MEMA, it is suggested that

(1) all input files, beta and more importantly t-statistic, come from 3dREMLfit output instead of 3dDeconvolve;
(2) warping to standard space be performed before spatial smoothing and individual subject regression analysis to avoid the troubling step of warping on t-statistic;
(3) no masking be applied at individual subject analysis level so that no data is lost at group level along the edge of (and sometimes inside) the brain.

More information can be found at [afni.nimh.nih.gov]

All feedback, + or -, and suggestions are most welcome.

Gang