st: Finite population correction when testing equality of two proportions

[Fredrik Nyberg <fredrik.nyberg@imm.ki.se>]

Hi all Statalisters

I am wondering about testing two proportions in the following setting:
Infinite overall population size (for all practical purposes)
Sample 1 taken from overall population
Sample 2 subsampled from sample 1

Now I want to test if the estimated proportion having a=1 is significantly 
different in sample 2 compared to sample 1.
True proportion in overall population is unknown.

Since these are not two independent samples from the same overall 
population, I think I need to adjust the test by making a finite population 
correction somehow for sampling sample 2 from sample 1. Only I can't find 
any details on this nor a test that appears suitable in Stata.

Can anyone help?
What is the correct test?
Is there Stata-code available?

Regards,
Fredrik

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