Dear AFNI team,

We are looking for guidance about how to compute something along the lines of a p value in the following situation.

Imagine that we have two conditions (A and B), and that for each we’ve established a 3D cluster map (relative to baseline), using an independent voxel threshold and a spatial extent threshold (following currently advised techniques; Cox et al., 2017). Further imagine that we interrogate each of these two maps within an ROI (e.g., L insula), and establish any cluster(s) for each map lying within it. Imagine, for example, that condition A activates a 70-voxel cluster within L insula above baseline, whereas condition B activates a 20-voxel cluster.

What we would like to establish is something like a p value for the probability of observing clusters of these two sizes within the ROI by chance (i.e., assuming that there is no underlying difference between the two conditions). In the example above, what is the probability of observing a 70-voxel cluster for condition A together with a 20-voxel cluster for condition B in L insula (again, when the two conditions are assumed not to differ)?

A potential wrinkle is that clusters could overlap within the ROI. In the example above, imagine that we assess overlap within L insula using a simple conjunction analysis, and find that there are 15 shared voxels between conditions A and B, along with 55 unique voxels for A and 5 unique voxels for B. Another form of our question could be what is the probability of observing this particular pair of unique voxel counts (55 and 5), again assuming no underlying difference between conditions?

Are there any AFNI tools for computing these kinds of probabilities? If not, do you have any suggestions for how to do so? Please let us know if any further information would be helpful.

Much thanks for your assistance! Best regards, Larry