When to use finite population correction?

Question

I'm looking to understand where we would and would not use finite population corrections: at what point would you draw the line and say that fpc is not appropriate?

I've read that it might not be used where n/N < 0.05. Are there other situations where it might not be used, eg a sufficiently large or unknown N?

I'm looking at a cluster sampling situation where N is unknown but could be estimated to around 100,000 and n/N > 0.05 using probability weighting from the known value of cluster sizes. I'm not certain what, if any fpc values to use when estimating population characteristics.

Answer 1

FPC is not necessary if you sample with replacement, don't care overestimating your standard error or you can assume your population is infinite (e.g. sample from a continuous distribution).

I think you should consider using FPC, in particular theories about cluster sampling generally add the term. Your population is finite, and your sample size is relatively large for the population size. I believe sampling software packages model the FPC (e.g. R's survey package) correction.