I have two matched groups consisting of 22 observations each for a Poisson distributed variable. I am interested in evaluating the power to detect a 20% decrease in the outcome for the second group. I have no idea of the correlation between matched groups and hence will have to assume independence. I am planning on evaluating the power using a simulation study and have the following ideas in mind.
1) Define rate0 and rate1 = rate0-(0.20*rate0)
2) Simulate X1~Poisson(22,rate0) and X2~Poisson(22,rate)
3) Compute pairwise differences X1-X2 and conduct a paired Wilcoxon test or a paired ttest.
4) Conduct simulation nsim times and compute the times pvalue < 0.05
I would appreciate some feedback/suggestions regarding step 3. Would anyone have any other ideas?