Mean centering my data for regression Can I mean-centre my data and then calculate the percentage change or is that redundant?
For instance, I want to perform a regression on my data. I have my participants IQ score, which I mean-centered (for my regression), but I want to calculate the change (or percentage change) in score over 2 timepoints. Can I do that after mean-centering or is that not correct?
 A: Note sure this is necessarily a regression question.  You have IQ scores on the same individuals, before and after an intervention, is that right? If so, you could calculate the percentage change for each person $i$, namely, $PctChange_i = 100(IQ_{i2} - IQ_{i1})/IQ_{i1}$. Then apply the usual types of techniques to the $PctChange_i$ data, such as point and interval estimation of the mean or median.  It would presumably be of interest to find out whether you can reasonably rule out zero as a possible value.
Dividing by a random quantity often introduces serious skewness into the distribution of the resulting fraction, but given that IQ's are typically far from zero, this might not be a problem here.
Also, if I have the scenario right, the $PctChange_i$ data might now be reasonably independent.  On the other hand, if you apply statistical techniques to the original IQ measurements $(IQ_{i1}, IQ_{i2})$, you will have to account for the dependence between them in your analysis.
All this is predicated on the repeated measurement scenario. Tell me that these are all distinct individuals and I will have to modify this answer substantially.
A: There is no issue in centering (or standardising preferably) your data before regression, but the percentage changes should be calculated from original IQ scores (if that makes sense anyway). Besides, you may have some numerical issues if you do it after centering, because somebody might have $0$ IQ.
