Dear Andrew,

Thank you very much for your helpful advice, if I may ask a couple clarification questions:

1. Does this mean that for e.g. a two sample independent t-test that:

A) running this twice (contrasts [0 1] and [0 -1]) as a t-test may actually give different results from
B) running this once as an F-test

Because in (A) the identified networks need to be homogenously greater or weaker in one group compared to the other, whereas in B) heterogenous networks are allowed.

In other words if the test-statistic network looks something like this toy example:

[[2, 2,  2,   1,  1],
[ 2, 2,  2,   1,  1],
[ 1, 1, -2, -2, -2],
[ 1, 1, -2, -2, -2],
[ 1, 1, -2, -2, -2]]

Then if using a NBS threshold of 1.5 using a t-test will find components of size 6 and 9, but a F-test would find a component of size 15 (allowing for the fact that the test statistic would be different, different NBS threshold needed for each approach). I think my previous incorrect intuition was that the F-test would just identify the larger homogenous component of size 9, which is what I thought would represent a 2-tailed t-test.

2. When thinking about a interaction effect I have the same general query - if one is wanting to identify homogenous interaction networks (e.g. if in the iq example we had patients and controls and we want to identify a network that gets stronger with iq in patients, and weaker with iq in controls or vice versa). Then would the way to do it have the design matrix of with columns of constant, iq, group, group*iq; and run two t-tests of [0 0 0 1] and [0 0 0 -1] as opposed to the single F-test?