Hi Alfonso,
Thank you very much for your response. I have a few follow-up questions as I want to be sure I understand and execute everything correctly if I move forward with this method.

1) To run the conjunction analysis in CONN, would I simply select Groups 1, 3 and 4 (in that order) and enter [-1 1 0]; [-1 -1 2] in the between-subjects contrast? 

2) As you said, the first contrast of the conjunction analysis will identify connections that differ between Groups 1 and 3 (i.e., Group1 - Group3). I'm a little less clear on the second part ([-1 -1 2]) -- will it identify connections that differ between Group4 and the combination of Group1 & Group3 (i.e., Group4 - (Group1+Group3))?

3) If I'm on track with part 2, above, then the conjunction analysis should return those connections that are different between Groups1 and 3 AND that are also different between Group 4 and (Group1+Group3) -- is that correct? If so, as you said in your initial response, we would interpret those results as connections where "the strength of the Group1vsGroup4 difference in connectivity differs from the strength of the Group3vsGroup4 difference in connectivity."

4) In your response, you said to "display those between-group differences in connectivity across these same connections in order to evaluate whether in fact the Group3vsGroup4 differences appear to be larger/stronger than the Group1vsGroup4 differences" -- would I just do that by calling up the results in the Results Explorer, selecting all of my ROIs, and using an analysis-level FDR correction?

5) Conceptually, I'm not clear how the conjunction analysis overcomes the potential bias due to different sample sizes. Can you say clarify that at all?

6) Would it be reasonable to add an additional covariate to this analysis, such as average framewise displacement? And if so, I assume I would simply select it in the subject effects menu and then add it to both parts of the conjunction analysis, as in [-1 1 0 0]; [-1 -1 2 0]. Does that seem correct?

Sorry about all of the questions. I really appreciate your help!

Best,
Jeff