Significance of overlap between multiple lists

Question

[gsmur]

I am trying to evaluate the significance of overlap between several lists of selected operational taxonomical units (OTU). Using several feature selection methods I selected OTUs relevant to a disease and I am trying to evaluate the significance of the intersection of selected OTUs based upon these methods.

My main goal is to show the significance of the core set of OTUs that were selected via multiple approaches.

Does anyone know how I could achieve this?

[gsmur]

I know that it can be done by this method for two groups but the issue here is for multiple groups. How do I evaluate the intersection between more than two groups.

Answer 1

[Asaf]

Fisher's exact test which uses hyper-geometric distribution to evaluate the significance of the intersection between two groups.

Answer 2

[Rubal]

Why not try permutations? For each approach you used randomly select the same number of OTUs. Do this a large number of times and then see how often you get the same number of overlapping OTUs just by chance.