Conjunction group analysis: An alternative to mixed/random effect analysis

We address the problem of testing in every brain voxel v whether at least u out of n conditions (or subjects) considered shows a real effect. The only statistic suggested so far, the maximum p-value method, fails under dependency (unless u = n) and in particular under positive dependency that arises if all stimuli are compared to the same control stimulus. Moreover, it tends to have low power under independence. For testing that at least u out of n conditions shows a real effect, we suggest powerful test statistics that are valid under dependence between the individual condition p-values as well as under independence and other test statistics that are valid under independence. We use the above approach, replacing conditions by subjects, to produce informative group maps and thereby offer an alternative to mixed/random effect analysis.