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st: Variance of ratio estimator

From   Marcello Pagano <>
Subject   st: Variance of ratio estimator
Date   Mon, 30 Oct 2006 10:42:59 -0500

Balduccio Attacchini would like to know:

I’d like to know the formula adopted by Stata in calculating the
variance estimator for ratio estimator in stratified single–stage design and with a finite population correction.
In particular, when I set
svyset_n, strata(..) fpc(..)
and then I run
svy: ratio y_total/x_total
The command returns an information labelled as 'Linearized Std. Err.'
The formula showed in page 263 of Survey data-Release 9(Stata) does not solve my question.
However the manual does not allow the case for Stratified single-stage design and Finite population correction (even the link to pag 259 is unclear being referred only to the variance estimation of a total).
So what is the formula behind the Linearized STd. Err. returned by the following commands?:
svyset _n, strata(..) fpc(..)
svy: ratio y_total/x_total

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