I am currently working with data from camera-trapping, where individuals from multiple species have been taken pictures of when they pass in front of one of the cameras (which are placed on a large area, about 2km apart from each other)
I expect the results (number of pictures taken, segregating by species and habitat type) to follow a Poisson distribution with an unknown parameter. My plan is to estimate it with sample means and then perform tests that check the equality between different habitats. I have tried non-parametric tests, but the samples are small and they don't have enough power
I am not sure, though, about the assumption of a Poisson distribution (it makes sense, but that doesn't mean it's true) When checking for variance among cameras in similar conditions, it consistently turns out to be slightly higher than the mean, which I guess is bad news. What could be a good way to test whether the data fits a poisson distribution or not? Also, what are the exact benefits, in terms of hypothesis test power, of "getting the distribution right" with regards to using non-parametric tests?
I know those are two separate questions, but they come from the same problem and I don't see any point in duplicating the above explanation in another post.
CLARIFYING NOTE: What I get is a dataset where each row indicates the date/time where a photo was taken, the species appearing on it, the camera that took the picture and the type of habitat where it is placed. Then I aggregate the data by both camera, species and day (thus aggregating the effect of day-night cylces), so that each camera-species-day count is a realization of a Poisson distribution (that depends only of habitat and species)