Hi Chen-Chia,

Thank you for your great question.

If you are interested in testing an individual effect (e.g. between-group difference in connectivity) when looking at the connectiity patterns across a single (or just a few) seed ROIs (i.e. looking at the connectivity between a single seed ROI -or a few seed ROIs- and many/multiple target ROIs) then I would recommend doing that directly in the main CONN gui 'second-level' results tab. Simply define there your subject-effects, between-subjects contrast, conditions of interest, and between-conditions contrast, and then select in the 'source/seed' list your desired seed ROI(s). That will perform a separate test for each target ROI. The degrees of freedom of that test will be F(n,m-n+1) where n is the rank of the kronecker-product of between-conditions and between-sources contrasts (typically this will just be equal to the number of seed ROIs), and m is equal to the number of subjects minus the rank of the design matrix (typically this will just be equal to N-1 for an individual between-subjects contrast). In the special case of a single seed ROI then the analyses will use instead a T- statistic instead of a F- statistic (a F(1,m) distribution is just is the same as a T(m)^2 distribution). You can double-check the degrees of freedom of the analyses by reading the "analysis results" table at the bottom of that same tab, or by clicking on the "design (n=...)" button, which will display your design matrix information (for an overview of second-level model specification see "Second-level analyses in CONN" in www.conn-toolbox.org/tutorials)

In addition to the above analyses, the "results explorer" tab allows you to perform other more complex analyses aimed at the scenario when you are interested in the same analyses but now across many/multiple/all seed ROIs (e.g. you may want to test an entire ROI-to-ROI connectivity matrix). The main limitation of the above procedure in this scenario is that, as one keeps increasing the number of seed ROIs included in the analyses, the F-statistic described above is going to eventually run out of degrees of freedom (n is going to be higher than m), or, well before that, is going to have very limited power/sensitivity. There are many ways to address that. In addition to other connection-level and network-level statistics, the "results explorer" window/GUI in CONN includes two main approaches for seed-level statistics in ROI-to-ROI analyses, one based on non-parametric analyses (Zalesky's network-based statistics) and another based on parametric analyses which is simply a variation of the original F-test above but performing first a dimensionality reduction of the connectivity patterns across all subjects and all of the seed ROIs simultaneously in order to limit the dimensionality of the data. This latter approach for dimensionality reduction is exactly the same approach used in the voxel-to-voxel MVPA analyses (but this time focused on ROI-to-ROI data instead of voxel-to-voxel data) which is described in the manual and in in www.conn-toolbox.org/measures. In these analyses, if the number of ROIs exceeds a threshold, then a PCA dimensionality reduction is first used to limit the number of components (and resulting degrees of freedom) of the corresponding F-test. The threshold is based on a a typical -but truly somewhat arbitrary- rule of thumb for reasonable power/sensitivity in these analyses (the rule of thumb says that one might expect to have at least about 5 times as many subjects as seeds (n>5*m) for reasonable power/sensitivity). This is why you are seeing in this case that "strange" behavior where the degrees of freedom of the F-test in the "results explorer" GUI are being capped at a maximum of 10 ~ 49/5. (when including additional ROIs CONN is performing a dimensionality reduction to limit the dimensionality of the data to 10 before performing the F-test). Unlike in the voxel-to-voxel MVPA, this ROI-to-ROI analyses do not allow you to manually specify the desired dimensionality of the resulting components (it just forces the number-of-subjects/5 choice). If you prefer a different choice you may do so programmatically by modifying the lines in conn_process.m and conn_display_roi.m that read "ndims=ceil(.." to your choice of target dimensions. 

Hope this helps
Alfonso
Originally posted by Chen-Chia Lan: