# 3 level, 3 group analysis advice

Dear AFNI hive mind -

I’d be grateful for your advice setting up/thinking about an analysis for the following design:

I have one factor with three levels (L0 L1 L2) and three groups of subjects (G0 G1 G2). I am interested specifically in those regions that vary monotonically across the three levels (either L2 > L1 > L0 or L0 > L1 > L2). I’d like to be able to ask: for those regions defined as showing a monotonic relationship in G0, how does the magnitude of that relationship within those same regions differ for G1 and G2? (Does G2 or G1 differ in magnitude relative to G0? Does G1 differ from G2?) Similarly, I’d like to ask which voxels over all show a group-level effect for this monotonic relationship.

If I had a four level design, I might specify a linear contrast such as [-1.5L0 -0.5L1 + 0.5L2 + 1.5L3] but that doesn’t make sense in a three level design because [-1 0 1] essentially compares the extreme levels and ignores the contribution of L1. I could set up a conjunction analysis in which I looked at which voxels survive a contrast both for L2 v L1 and L1 v L0 but I don’t know how I would quantify the magnitude of that conjunction effect for comparison between groups (sum of betas?) or how to determine the FDR for such a conjunction map.

Thanks for your input/feedback!

With three levels, there are no easy solutions to make inference about their monotonic relationship other than pairwise comparisons. You can use 3dMVM with -gltCode to obtain the contrasts of L2 v L1 and L1 v L0, and then check their overlap.

how to determine the FDR for such a conjunction map

The conventional approach is to adjust for multiple testing before, not after, the conjunction analysis. In addition, check out this discussion: https://afni.nimh.nih.gov/afni/community/board/read.php?1,166126,166126#msg-166126