This is an elementary question, but I wasn't able to find the answer. I have two measurements: n1 events in time t1 and n2 events in time t2, both produced (say) by Poisson processes with possibly-different lambda values.
This is actually from a news article, which essentially claims that since $n_1/t_1\neq n_2/t_2$ that the two are different, but I'm not sure that the claim is valid. Suppose that the time periods were not chosen maliciously (to maximize the events in one or the other).
Can I just do a t-test, or would that not be appropriate? The number of events is too small for me to comfortably call the distributions approximately normal.
Best Answer
To test the Poisson mean, the conditional method was proposed by Przyborowski and Wilenski (1940). The conditional distribution of X1 given X1+X2 follows a binomial distribution whose success probability is a function of the ratio two lambda. Therefore, hypothesis testing and interval estimation procedures can be readily developed from the exact methods for making inferences about the binomial success probability. There usually two methods are considered for this purpose,
You can find the details about these two tests in this paper. A more powerful test for comparing two Poisson means