I have a problem regarding my data for an ANCOVA. I conducted an experiment with a 2x2 between subjects design (4 different treatment groups) and covariates. Due to the treatment I was just able to ask for the covariates at the end of the experiment. I know that covariate and independent variable have to be independent but in my case unfortunately one covariate was influenced by the treatments. The problem is that I really need this covariate for my analysis. My idea was to partial out the treatment effect from the covariate (run a linear regression on the covariate with the treatments as independent variables and save the residues). Then I want use the residues as “new” covariate in my ANCOVA. But I don’t know if this is an approved approach. So is it possible to run an analysis like that? And is this an established solution? If not, is there an alternative method or do I have to omit the covariate?
You may have a look at this paper: http://psycnet.apa.org/journals/abn/110/1/40/ (Misunderstanding analysis of covariance). I believe that the answer is that once groups differ in the covariate, you cannot use it meaningfully.