Sorry, I'll start over just to make sure everything is clear.

I have 20 participants. Ten of them did Task 1 on Day 1 and Task 2 on Day 2. The other ten did Task 2 on Day 1 and Task 1 on Day 2. We collected resting state scans before and after each Task. I'll refer to them as pre-Task1 scan, pre-Task2 scan, post-Task1 scan and post-Task2 scan (This is 'Time' factor).

I am interested in differences in resting states before and after each task (so essentially a Task x Time issue). But I want to model as much as possible and strip away any confounds.

1. So, my first question was whether my ANOVA should be Task (Task 1 versus Task 2) x Time (pre versus post) and whether I can use Day (Day 1 versus Day 2) as a covariate to strip it away. It is not technically exactly as Task because of the split between subjects. Am I wrong about this?

2. Group (ten subjects versus ten subjects) is not a factor of interest - we split them up to 'wash-out' as much effects of Day. Do you still think I should use Group as a covariate?

3. I'm not sure the reaction times vary across our Tasks. I can check. Do I use them as covariates only if they do vary?

Thanks for the help. Really appreciate it.