# Re: st: Confidence Interval for Proportion

 From jpitblado@stata.com (Jeff Pitblado, StataCorp LP) To statalist@hsphsun2.harvard.edu Subject Re: st: Confidence Interval for Proportion Date Tue, 11 Mar 2008 13:08:17 -0500

```Martin Weiss <martin.weiss@uni-tuebingen.de> is using the -proportion- command
and has a question about how standard errors are computed:

> Dear Statalisters,
>
> try this in Stata:
>
> ************************
> sysuse auto, clear
> proportion rep78
> matrix define A=e(b)
> matrix define B=e(V)
> count if rep78!=.
> *Upper/Lower Bound for proportion of "1"
> di A[1,1]+invnormal(1-0.05/2)*sqrt(A[1,1]*(1-A[1,1])/`r(N)')
> di A[1,1]-invnormal(1-0.05/2)*sqrt(A[1,1]*(1-A[1,1])/`r(N)')
> *Standard Error for "1"
> *Mistake obviously there...
> di sqrt(A[1,1]*(1-A[1,1])/`r(N)')
> ************************
>
> Then let me know: why do I not hit the correct CI for the proportion of "1"
> in the repair record? Something`s wrong with the standard error, I do not
> know what, though...

Using Martin's example Stata code, -proportion- effectively computes the
standard error via

sqrt(A[1,1]*(1-A[1,1])/(r(N)-1))

This is explained (rather tersely, I'll admit) in the 'Methods and Formulas'
section of -[R] proportion-.

"Proportions are means of indicator variables; see -[R] mean-."

```