I m performing an analysis with the following data: I have 2 groups (38 patients and 27 controls) and a variety of cognitive tests. These groups have differnet intelligence scores and I would like to handle their intelligence score as a covariate. However, the ANCOVA prerequisite of homogeneity of regression slopes is not met. So, I wonder whether there is another way to handle this difference in intelligence scores. I have read that regression is an alternative but how is it possible to run a similar to ANCOVA regression as my independent variable is categorical (patients  and controls). is a logistic regression the solution? 

Furthermore, I would like to run a mixed ANOVA with group as the independent variable and three cognitive measures as the within subjects variable. The 3 within subjects cognitive measures have slight differences in scoring (all numerical, but with different minimux-maximum values). I m not interested in the differences between these 3 measures but in the interaction groupX cognitive variable. Which is the best method to proceed? May I perform an ANOVA using raw scores or should I perform it with z scores? I have already try both and I m getting different results (I get a significant groupX cognitive variable interaction with raw scores  and a not significant interaction with z- scores). 

Thank you in advance.