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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?

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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.

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  • $\begingroup$ Thank you for your reply. Is it weird to report that the F-value of covariate is 0 and the sum of square is also 0? That's my case. $\endgroup$
    – Pancy
    Feb 15, 2015 at 21:24
  • $\begingroup$ It's hard to say what's going on there. I don't know how your SS could be 0 unless your covariate is a constant. $\endgroup$
    – gung - Reinstate Monica
    Feb 15, 2015 at 21:37
  • $\begingroup$ This is the most strange thing to me, since it is obviously not a constant! Someone suggests that maybe the covariate is completely not correlated to the variables (but I don't think correlations between variables would affect SS). $\endgroup$
    – Pancy
    Feb 16, 2015 at 1:02

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