I have conducted a repeated-measures ANOVA, but a reviewer suspects that the observed main effect of condition are due to a the difference between hit rates of two conditions (one of them is significantly higher). Therefore, he suggests to do a ANCOVA.
I used the difference between hit rates as a covariate and do the ANCOVA. However, the distribution of the covariate is skewed and obviously violates the assumption of normal distribution of covariate in ANCOVA. All other variables are normally distributed.
I have tried changing all data into rank and put them into ANCOVA in SPSS (try to mimic a non-parametric test in SPSS), and failed (because changing the difference into rank makes it evenly distributed, not normally distributed). In principal, changing the covariate into z-score will not change the distribution.
What can I do?
Best Answer
ANCOVA is a special case of a multiple regression model. Multiple regression does not make any assumptions about the distributions of the explanatory variables / covariates (for more information see here: What if residuals are normally distributed, but y is not?). Therefore, you are OK; you don't need to do anything to your covariate—just use it.