Poisson or Binomial distribution for modeling? I want to model the change in rate of an event in a sampled population. The populations are grouped according to some grouping variable. Each individual observation is of one organism, and the sample can either return as positive or negative (+/-). My resulting parameters are:
-number of positive samples (+)
-total number tested per grouping variable
Should this be modeled using a Poisson or binomial distribution? My sample parameters are meant to estimate the true rate value in an overall larger population.

Poisson and Binomial distributions both model the counts of events.
The Binomial distribution is about the number of counts of events in a sequence of experiments that measure a boolean valued outcome. The events can only occur on a fixed number of cases/experiments.
The Poisson distribution is about the number of counts of events in an interval of time or space. The events can occur continuously.

See also on Wikipedia:
https://en.wikipedia.org/wiki/Poisson_distribution

In probability theory and statistics, the Poisson distribution (/ˈpwɑːsɒn/; French pronunciation: ​[pwasɔ̃]), named after French mathematician Siméon Denis Poisson, is a discrete probability distribution that expresses the probability of a given number of events occurring in a fixed interval of time or space if these events occur with a known constant mean rate and independently of the time since the last event.

https://en.wikipedia.org/wiki/Binomial_distribution

In probability theory and statistics, the binomial distribution with parameters n and p is the discrete probability distribution of the number of successes in a sequence of n independent experiments, each asking a yes–no question, and each with its own Boolean-valued outcome: success (with probability p) or failure (with probability q = 1 − p).

