How would I statistically test the significane of the difference between two Cohen's d derived from different tests within the same sample?
Specifically, in my neuroimaging data metabolism in brain region A is reduced by 10% (with d=0.8) in a patient group compared to a control group, and metabolism in region B is reduced by 15% (with d=1.2). Both findings are highly significant. How would I test if the effect in region B is significantly bigger than in region A.
A similar problem has been solved for effects sizes derived from independent samples in the context of meta-analyses: Statistical comparison of 2 independent Cohen's ds but I'm not sure how this would change for effect sizes corresponding to different tests within the same sample.
By searching the archives I have found a similar question, but it hasn't been answered: How to assess whether two treatments are significantly different using Cohen's d (effect size)?