Thank you, Gang!

As you said, I definitely want to control for the variability of RT, and clean out its contribution from the overall variability. Because of collinearity, as you said, I should center within each condition, no matter how I do it. I just wonder about two things (and perhaps I just didn't fully understand your previous answers, so my apologies if so):

1. If the point is removing irrelevant variability from the data and I'm not interested in RT per se, why should I put it as a random effect and not a fixed effect in the first place? It seems more relevant to put Cond as the random effect (adjust it by subjects).

2. I actually have Cond1 (2 levels) and Cond2 (2 levels). So the fact that I have four RTs per subject - one per Cond1*Cond2 combination - is unclear to me... Can RT be both a within- and a between- predictor? If so then this is new to me, I can't think how this is implemented mathematically. After centering, we expect no within-subject effect of RT anyway. So why don't we just give one number which is the average for each subject (across Con1 and Cond2), thus it is just a between-subject covariate?

Thanks,

Galit