Hi Gang,

I have thought more about my research question and have a few follow-up questions that I hope to get some help on. For context: I have 2 groups (HR: high risk for autism; LR: low risk for autism) with an uneven number of subjects in each group. I'm interested in the difference in amygdala functional connectivity between the groups, as well as how Brain Volume (continuous variable) is associated with connectivity. In total I have 3 covariates of no-interest as I mentioned in my initial message (Site, Maternal Education, Father's Age), and also 1 covariate of interest (Brain Volume). This leads me to two follow-up questions:

1) I was reading through the documentation on 3dttest++, which states that "Only the -paired and -pooled options can be used with covariates." I cannot run a paired t-test (since I have an uneven number of subjects in each group) and I want to avoid the subtraction technique described in the documentation. Would it be better/appropriate to use 3dMVM (since I can incorporate covariates there too)?

2) Regarding centering for the continuous covariates: Father's Age is significantly different between the two groups (and I would like to "regress out" the effect of this covariate), but Brain Volume is not significantly different between the two groups (however, I expect the relationship between Brain Volume and amygdala functional connectivity to be different between the two groups; this is a covariate of interest). I have revisited this helpful link, but wanted to check - would it make sense to not demean either variable? Or would it make more sense to demean Brain Volume (since I expect the slopes to be different between the two groups) but not to demean for Father's Age (since I want to regress out the effect)? I'm a little lost at this point thinking through the potential possibilities! What would you recommend in terms of centering as I know that it strongly impacts the interpretation?

Thank you very much!
Janelle