Indeed, this do-file illustrates the problem for all five categories
************************
sysuse auto, clear
qui{
proportion rep78
matrix define A=e(b)
count if rep78!=.
forv i=1/5{
local stderr`i'= sqrt(A[1,`i']*(1-A[1,`i'])/`=`r(N)'-1')
noi di in red "Standard Error for `i':" _column(27) as result `stderr`i''
noi di in red "Lower Bound for `i':" _column(27) as result
A[1,`i']-invnormal(1-0.05/2)*`stderr`i''
noi di in red "Upper Bound for `i':" _column(27) as result
A[1,`i']+invnormal(1-0.05/2)*`stderr`i'' _newline
}
}
*For Comparison
proportion rep78
************************
Martin Weiss
_________________________________________________________________
Diplom-Kaufmann Martin Weiss
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-----Original Message-----
From: [email protected]
[mailto:[email protected]] On Behalf Of Jeff Pitblado,
StataCorp LP
Sent: Tuesday, March 11, 2008 7:08 PM
To: [email protected]
Subject: Re: st: Confidence Interval for Proportion
Martin Weiss <[email protected]> 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-."
