# RE: st: Confidence Interval for Proportion

 From Maarten buis To statalist@hsphsun2.harvard.edu Subject RE: st: Confidence Interval for Proportion Date Tue, 11 Mar 2008 22:01:52 +0000 (GMT)

```Martin may have a point, though I am not sure: I have always taught
that the reason we compare the test-static to the t-distribution and
not the Gaussian distribution is that we have additional uncertainty
due to the fact that we not only estimate the mean but also the
standard devation (to get to the standard error). In case of a
proportion we know that the standard deviation is a deterministic
function of the mean, so why should we compare the test-statistic to
the t-distribution instead of the Gaussian distribution?

-- Maarten

--- Martin Weiss <martin.weiss@uni-tuebingen.de> wrote:

> Jeff,
>
> thanks for the reply, but am I still missing something here? I did
> experiment with the " r(N)-1", but discarded the possibility as it
> did not
> provide the correct lower and upper bound... Indeed,
>
> ************************
> sysuse auto, clear
> proportion rep78
> matrix define A=e(b)
> count if rep78!=.
> *Std error
> local stderr= sqrt(A[1,1]*(1-A[1,1])/`=`r(N)'-1')
> *Upper/Lower Bound for proportion of "1"
> di A[1,1]+invnormal(1-0.05/2)*`stderr'
> di A[1,1]-invnormal(1-0.05/2)*`stderr'
> ************************
>
> still gives the wrong numbers. Have you told us the whole story?
>
> Martin Weiss
> _________________________________________________________________
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>
>
> -----Original Message-----
> From: owner-statalist@hsphsun2.harvard.edu
> [mailto:owner-statalist@hsphsun2.harvard.edu] On Behalf Of Jeff
> StataCorp LP
> Sent: Tuesday, March 11, 2008 7:08 PM
> To: statalist@hsphsun2.harvard.edu
> Subject: Re: st: Confidence Interval for Proportion
>
> 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-."
>
> From the 'Methods and Formulas' section of -[R] mean-, the variance
> is
> calculated as
>
> 	V(ybar) = (1/(N*(N-1))) Sum_{j=1}^N (y_j - ybar)^2
>
> If the y_j are observations of an indicator variable, this is
> algebraically
> equivalent to
>
> 	V(ybar) = ybar(1-ybar)/(N-1)
>
> --Jeff
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-----------------------------------------
Maarten L. Buis
Department of Social Research Methodology
Vrije Universiteit Amsterdam
Boelelaan 1081
1081 HV Amsterdam
The Netherlands

Buitenveldertselaan 3 (Metropolitan), room Z434

+31 20 5986715

http://home.fsw.vu.nl/m.buis/
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