What is the difference between a finite population and an infinite one - when you are designing an experiment (sample/power and interpretation of the results)?
Say a company has a database of 20,000 customers. Given that a response to some stimulus is relatively small, and a meaningful minimum detectable difference is also small, if you run a power analysis for a 2 sample proportion, you may find that you need 2 groups of 15,000 for the experiment.
Do you quit and say you cant experiment on this population? Or do you (somehow) instead treat the population as finite and run a power analysis that way? What are the implications?
What I would like to know, and wanted to add this detail in case the last part of the question wasn't completely clear - is what the difference is between
The inference with assuming an infinite population, say the inference from a logistic regression model with
The inference with assuming a finite population, say inference from a logistic regression model with svyglm in R?
Will #1 allow inference about the wider population / data generating process and #2 only allow inference about that particular population (which is assumed fixed)?