If I have a series of populations, and a set of outcomes for these populations, how can I be certain that the observed proportions are, in fact, credible?
I have investigated certain sampling methods to see if I can manipulate formulae to come up with a rule - but this feels quite crude. Is there some mathetical theorem/principle that I have missed?
If I have a population of 1000 with a 'good' outcome of 231, compared with a population of 10 with an outcome of 4; how do I define which result is accurate? (note: these are not samples, they are populations)
Intuitively, I would say that a population of 10 is not sufficently large to draw an accurate result - but how can I define this 'limit' of accuracy?
I've played around with the sample size formula for a hypergeometric function, but that's as far as I've got. There also seems to be a lack of literature on dealing with small population sizes. Any ideas?
I really appreciate the help.