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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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