# Mean difference for count data

I have two samples $s_1$ and $s_2$ of count data. The sample size is > 1000 each. The distributions look similar to a Poisson distribution but the variance is much larger than the mean.

How do I test whether the mean of $s_1$ is larger than the mean of $s_2$?

• What are the counts? Are they all small numbers or do they vary over a wide range? – Peter Flom Oct 11 '13 at 20:13

I would suggest you fit a Poisson or loglinear regression model with just one dummy variable created for the two groups and then test the slope parameter, say, $H_a: \beta_1 >0$. Any test method (LRT, Wald, or score) under the maximum likelihood framework can be used. As for over-dispersion problem, you may consider other count models such as negative binomial or generalized Poisson models. This should essentially give you a two-sample test for count data.