I know there are similar posts, and I've read a few of them already, but none of them give explanations that I actually understand. I'm completely new to statistics and am finding it more difficult that there seems to be many versions of tests suggested when comparing 2 poisson distributions. The worst part, is I'm not even sure if my data follows a poisson distribution and am not sure how to find out.
My problem is simple: I've got counts of mutations within a specific gene (of a specific length) that I'm looking at totalled over a population of patients. Assuming mutations are random, my null hypothesis expects that the rate at which this specific gene gets hit would be the same as any other gene (so I'm comparing it against all mutations over all genes of all patients vs all mutations landing only on a specific gene). I'm getting the rate simply by dividing the total number of mutations, over the length of the gene (in bases). Numbers are extremely small and rates are something like 2x10^-5 (for the specific gene) and 7x10^-6 (for all mutations in all genes totalled). I just want to compare to see if the rates I'm getting are significantly different from each other. That is the whole goal.
Am I even looking in the right direction by googling poisson distribution? The rates are extremely small which is why I thought to google "statistics of rare events" and came across poisson in the first place.