Dear Dr. Alfonso,

Hope you are doing well! I have a few questions regarding the omnibus tests being performed as part of the ROI-ROI FNC analyses.

Background:

- Conn 20.b, SPM12 7771, MATLAB R2016a
- 39 healthy subjects, 57 patients
- task fMRI where I am currently looking at one condition which is of interest
- analyses performed in the same space as functional (which are normalized to MNI space with 3mm isotropic voxel size)
- HRF-weighted correlation based ROI-ROI connectivity using Schaefer 7 networks 100 parcels atlas
- second level ROI-ROI FNC (with standard settings)
- specifying custom grouping file where the parcels are grouped as per the 7 networks

What I think is being done during FNC:
- since there are 7 ROI groups, therefore there are nchoosek(7,2) = 21 between network clusters and 7 within network clusters = 28 clusters (which is what I see in the GUI with clusters going from 1-28)
- For each of the 28 clusters, perform a multivariate GLM where Y = all pairwise connections between ROIs within a cluster, X = ones(n,1) [in case of one sample test, where n is the sample size] OR X = [[ones(N1,1); zeros(N2,1)], [zeros(N1,1); ones(N2,1)]] for a between group comparison, where N1 and N2 are sample sizes and the contrast will be specified as [1, -1]
- The omnibus test is followed by a series of t-tests for each pair of connections within the cluster

Questions:
Is it correct to say that for each cluster, the omnibus test is "are there any pairs of connections within this cluster for which the mean connectivity is not zero" (for a within group test) OR "are there any pairs of connections within this cluster where the mean connectivity difference between the two groups is not zero" (for between group test)?

As a specific example, say my first cluster consists is the DMN; there are 24 ROIs in the DMN group. Therefore, there would be 276 pairs of connections within this cluster. For within group comparison for healthy subjects, the GUI shows me a F(2,37) = 696.19. If I stack up my connectivity values as a 39 x 276 DMN_HS matrix, then can the F statistics can be obtained as: [h,F,p,dof,statsname]=conn_glm(ones(39,1),DMN_HS)? Similarly, the between group omnibus degrees of freedom are (3,92).

Perhaps I am misunderstanding the omnibus tests being done here? Could you provide some clarification/insights on the omnibus test being performed and how the degrees of freedom are being calculated above? Thank you very much for your time and help.


Warm Regards
Pravesh