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Re: st: FPC & 2-stage cluster sampling

From (Jeff Pitblado, Stata Corp.)
Subject   Re: st: FPC & 2-stage cluster sampling
Date   Tue, 03 Jun 2003 16:45:34 -0500

Ali Karim <> asks about 

> I have a dataset with two-stage cluster sampling. In first stage 30 PSU’s
> were selected randomly (without replacement) from a universe of 60 clusters
> (i.e. fpc = .5). On the second stage 30 households were selected randomly
> from each PSU. I planned to analyze household attributes using Stata’s
> ‘svy’ commands. I did the following:-
> .svyset psu cluster
> .svyset fpc frac
> And then run my survey commands. The output gave me the following comment:- 
> “Finite population correction (FPC) assumes simple random sampling without 
> replacement of PSUs within each stratum with no sub-sampling within PSUs”. 
> However, the assumption does not seem to hold for my sampling design. 
> Therefore, I am not sure how the assumption affects my analysis. Am I using 
> the survey command correctly for my given situation?

If your design includes sampling within the PSUs, then you should not use the
Finite Population Correction (FPC).  Otherwise, the variance estimates will be
negatively biased (too small).

Lets look at a specific design to see why:

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