Your approach won’t work I’m afraid because the conjunction null is that (for 2 maps) that 0 or 1 of the maps is null, that is, to have a valid conjunction inference you have to allow for the case where one effect is present (very strong even) and the other is null. This won’t be reflected in a permutation test where both null hypotheses are assumed to be true.
So, actually, one type of cluster conjunction infernece is easy to impliment, but it rarely has power to detect anything: You determine what is the cluster size significance threshold for each null map, and then you use that critereon on the clusters found in the intersection map.
- Run a usual permutation test for effect 1, call it T1, and effect 2, T2, with the same cluster forming threshold, call it u. Call the binarised maps T1u and T2u, e.g.
- Determine what would be the minimum significant cluster size, i.e. the 5% FWE cluster size threshold. It won’t be identical for the two maps, T1 & T2, but you can take the more conservative (larger cluster size thershold) of the two. While randomise doesn’t directly produce this number, you can find it by useing the
-N option, which will produce the null distribution of maximum cluster size, and the 95% percentile will be the critical cluster size threshold, call it
u2 respsctively. Taking the larger of the two,
- Take the intersection of clusters in T1u and T2u,
Tconj = T1u*T2u, and compute clusters (e.g. with FSL’s
cluster); any clusters larger than
uconj are significant.
In my experience the intersection map clusters are always so much smaller that this approach rarely finds anything, but it willl give you a proper conjunction inference.