Thank you Andrew and Alfonso.

Andrew, in your most recent comment you've stated: "In terms of orthogonality, I don't really see this as two nested tests (although I definitely understand your point). For example, the first test (one-sample) can be performed on an independent set of controls to which the second test (two-sample) is performed."

I appreciate that if you have conducted a one-sample test on an independent set of controls that the issue of nested tests is not a problem for the group differences test. But what about if you do as I suggested in my previous comments, where we would include connections that differed in either the diseased group and/or the control group, and then conduct the two-sample test on these connections? This seems to be the test sets that Alfonso is concerned about ("Y>0, or [0 1]) is not orthogonal to the main contrast (Y-X>0, or [-1 1]") If I'm understanding correctly. Is it sound to threshold the network based on group differences in either group (i.e., connection ~= 0 in diseased or controls), and then conduct the group-level test on only these connections?

Thank you!