# Re: st: Different confidence intervals from proportions and tabulates (also in survey)

 From jpitblado@stata.com (Jeff Pitblado, StataCorp LP) To statalist@hsphsun2.harvard.edu Subject Re: st: Different confidence intervals from proportions and tabulates (also in survey) Date Sun, 29 Oct 2006 16:51:32 -0600

```Jason Ferris <J.Ferris@latrobe.edu.au> is concerned that the confidence
intervals from -svy: proportion- are different from -svy: tabulate- even
though the point estimates and standard errors are the same:

> Hi. I have been running survey proportions and observing results with
> negative confidence intervals (which doesn't make sense).  When I use
> survey tab (with column percent, se and ci) I get the same point
> estimates and standard errors but different 95% confidence intervals.  I
> assume this is an issue with the proportion calculations using "Binomial
> Wald" for confidence intervals.
>
> I checked the survey manual and have not been able to find why:
>
> Paste the following command to see my dilemma:
> webuse nhanes2b, clear
> svy: proportion race
> svy: tab race, ci se
>
> The results show the same point estimates and standard errors (with
> rounding) but different CI's.  As mentioned, for my data, I get some
> negative CI's for svy: proportions commands but not for the svy:
> tabulate commands. My ultimate concern is being able to automatically
> extract the CORRECT estimates to excel (from using matrix e(b) and e(V)
> - and calculating 95% CI from square-root of e(V) *1.96).
>
> I am using the latest version of Stata 9.2, on Windows XP.

While -svy: proportion- uses the normal approximation formulas for confidence
limits, e.g.

phat +/- sehat*t_critical_value

the -svy: tabulate- command uses a logit transform.  The benefit of using the
logit transform is that the confidence limits are guaranteed to stay within
the parameter space for a proportion, i.e. [0,1].

The formulas for the logit transformed confidence limits used by
-svy: tabulate- are documented in the 'Methods and formulas' section of
'[SVY] svy: tabulate twoway'.

--Jeff