Re: centering, thank you for sharing the link! Based on the section "When to center within- or across-groups?" it seems like the overall idea there is to use centering to get rid of within-group variability in order to better examine between-group differences. In my case, the covariate of no interest is not linked to group status and my goal isn't to necessarily get rid of within-group variability in motion, but rather to get rid of between-group differences in motion to ensure that my group differences cannot be attributed to differences in motion. It seems that if I were to center the motion variable within-group then I would be eliminating within-group variability, but that wouldn't address the between-group differences in motion. In order to best eliminate between-group differences in motion (continuous covariate of no interest), I think I would still have to demean across all groups?

Thank you!
Janelle