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Context:

This is the design:

  • 11 patients were examined for a "Response Parameter" before and after a specific treatment.
  • 12 healthy control patients were examined for the "Response Parameter" (did not receive treatment).

The numbers included are rather small and the "Response Parameter" may not be normally distributed, which is why I think non-parametric statistics is better.

So, I want to test the Null Hypothesis:

"There is no difference in "Response Parameter", also after adjusting for age and gender."

I am using R. The variables are "Group", "Age", "Gender", "Response"

Question:

  • How do I do I test this hypothesis?
  • Is ANCOVA using ranked "Response Parameter" appropriate?

Because the measurements on the 11 patients are paired (before and after treatment), I doubt I can use ANCOVA at all.

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Note that in such a paired setting it is sufficient that the differences in the response be normally distributed (specifics depend on how you set up the analysis). –  Aniko Oct 5 '11 at 14:36
    
"adjusting for age and gender" sounds like your covariates are correlated with the other predictors, which violates the assumptions of your analysis. ANCOVA is supposed to be a means of enhancing statistical power, it is not a means to eliminate confounds in your data. See: stats.stackexchange.com/questions/4551/… –  Mike Lawrence Oct 5 '11 at 17:35
    
I was asked to this analysis by a reviewer, but recognize that the use of ANCOVA to correct for age and gender may not be correct. At least covariates do not heavily correlate with predictors (rho<0.20). Can I analyse on one paired set of data + one control group within one ANCOVA? What post-hoc test would be best? –  user4229 Oct 6 '11 at 9:50
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