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Re: st: generating confidence intervals from weighted (survey) data

From   Maarten buis <>
Subject   Re: st: generating confidence intervals from weighted (survey) data
Date   Mon, 17 Aug 2009 07:07:45 +0000 (GMT)

--- On Mon, 17/8/09, Peter Ittak wrote: 
> I have weighted survey (categorical) data from which I wish to
> generate confidence intervals (CIs). I use the -svyprop- and 
-svymean- commands and I get confidence intervals no problem.
> Stata uses Wald binomial calculations. But when N is small
> (proportion < 0.01 (percentage < 1%)) Wald calculations are
> not appropriate (Stata happily still calculates them though).
> I could use exact calculations (cii command) but this is an
> appropriate solution only when survey data is approximately
> self-weighting. But my data is *not* approximately
> self-weighting, not by a galactic mile.
>  For *fun*, I tried using
> the cii command but sometimes (not surprisingly) I got weird
> results, such as 0.2% (0.5% - 1.1%) where 0.2% was the
> weighted point estimate obtained from svy commands and 0.5%
> - 1.1% was the CI from exact calculations (using cii
> command). Indeed, this was not a good look!
>  Does anyone know of any *analytic* methods to
> solve this problem? (as opposed to using bootstrap
> techniques)
>  I am interested in analytic techniques (assuming these are 
> available) because I have other instances where my results
> are sometimes 100%, and sometimes 0%. Stata is not able to
> generate CIs for such results (remember, svy commands are
> being used because the data is weighted) and boostrap
> methods are useless here because all that one does when
> using bootstrap techniques is resample 100% (or 0%) over and
> over again without any uncertainty.

Any method for calculating confidence intervals of a proportion, 
including the "exact" method, will get the coverage somewhat 
wrong, especially when you have such small proportions. Given 
this I would not waste too much effort on getting the estimated 
confidence interval exactly right, but instead pick a reasonable 
one and treat it as a roughly accurate indication. There is some 
evidence that the approximate methods actually do a better job 
than the exact methods: 

Agresti, Alan, and Coull, Brent A. Approximate is better than 
'exact' for interval estimation of binomial proportions. The 
American Statistician 52: 119-126, 1998.

Hope this helps,

Maarten L. Buis
Institut fuer Soziologie
Universitaet Tuebingen
Wilhelmstrasse 36
72074 Tuebingen


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