  # st: comparing equality of count responses

 From cschecht@aecom.yu.edu To statalist@hsphsun2.harvard.edu Subject st: comparing equality of count responses Date Sun, 13 Feb 2005 15:51:01 -0500

```Just got back from out of town and went through a week of statalist-digests.
Early last week somebody asked about testing the equality of count responses
when the variables are Poisson in two groups, and I didn't see any response to
it.

I'm interpreting this as meaning that in each of two groups i = 1, 2, there is
a Poisson process operating with parameters mu1 and mu2, respectively.  The
question is how to test the hypothesis mu1 = mu2 after observing n1 and n2.
Given two Poisson processes, it is easy to show that conditional on n1+n2, n1
~ Binomial(n1+n2, p) where p = mu1/(mu1+mu2).  In particular, if mu1 = mu2, p
= 0.5.  So to test mu1 = mu2, just see where n1 falls on the binomial
distribution with parameters n1+n2 and 0.5.

Hope that's what you were looking for.

Clyde Schechter
Albert Einstein College of Medicine
Bronx, NY, USA

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