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st: comparing equality of count responses
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
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.
Albert Einstein College of Medicine
Bronx, NY, USA
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