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I have two processes that produce the same type of event. For example, after 48 hours I may have 10,321 events from one process and 11,548 events from the other.

What statistical test do I use to determine the chance that Process B produces events at a faster rate than Process A?

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  • $\begingroup$ One way to begin clarifying this problem is to note that over that particular 48 hour time period, the other process produced more events--period. There's no chance involved in that statement. If you are uncertain, then, it could be because (a) you're not sure the data are accurate or (b) you would like to make an inference about how the processes perform in other time periods. In either case you cannot proceed without assumptions: exactly how could the data be in error and exactly how would the process counts be related to one another during different time periods? $\endgroup$
    – whuber
    Commented Aug 5, 2015 at 13:15

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There are a number of approaches that could be taken.

Perhaps the simplest would be to condition on the total number of events. Then if the events were each being produced independently at a constant rate, under the null hypothesis of equal rates the 'true' population proportion of events of each type is 0.5.

One can simply run a binomial test.

However, a hypothesis test doesn't tell you "the chance that Process B produces events at a faster rate than Process A". It would allow you to reject the null against a directional alternative (or a two-tailed alternative if you didn't know beforehand which one you expected should be faster), but not give an unconditional probability statement.

If you want a statement of the form "probability B is faster than A" you'd need to perform a Bayesian analysis with some model for the rates, and with a prior on that probability.

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