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I have two populations of earthquakes that happened in the same area, the Mediterranean Sea, but in different time periods. The first gives me a rate of 27 per day, and the second 40. How can I test whether this difference is significant?

Silverfish
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I believe the question you are asking is how to check whether observations of 2 different Poisson processes have different means. Several possibilities are given here:

Checking if two Poisson samples have the same mean