I have many subjects that were cluster-randomized to a treatment group and to a control group. I want to check the age balance of the groups following the randomization - e.g. whether there is a difference in the mean age in the two groups. I have a wide range of ages in our sample and each of the two groups, with a large number of subjects but only about 50 clusters in each of the two groups.
I used a two-sample t-test and found a minimal difference between the two groups and p=0.22 or so. My concern in using the t-test is that the dependent variable is likely better modeled as a Poisson distribution. So, I ran a Poisson regression with an intercept and a dummy variable for group membership. It's hard for me to think about expected counts in substantive terms, but p=0.06 or so.
It seems odd to me that I would have such different results from the two approaches.
- Is the Poisson regression not merely testing for differences in expected counts as opposed to differences in expected means of a continuous variable for the t-test?
- Is it appropriate to model age as a count variable? Is it questionable to model it as a normally distributed variable?