# st: RE: RE: Confidence Interval for Proportion

 From "Lachenbruch, Peter" To Subject st: RE: RE: Confidence Interval for Proportion Date Tue, 11 Mar 2008 09:42:05 -0700

```For small proportions, the exact option is useful.  It is the standard
that the other methods hope to reach.  Coverage is exact.
Agresti and Coull have a nice paper (I don't remember the attribution,
but I think it's American Statistician, somewhere around 2000).

Tony

Peter A. Lachenbruch
Department of Public Health
Oregon State University
Corvallis, OR 97330
Phone: 541-737-3832
FAX: 541-737-4001

-----Original Message-----
From: owner-statalist@hsphsun2.harvard.edu
[mailto:owner-statalist@hsphsun2.harvard.edu] On Behalf Of Nick Cox
Sent: Tuesday, March 11, 2008 7:05 AM
To: statalist@hsphsun2.harvard.edu
Subject: st: RE: Confidence Interval for Proportion

The "correct" CI for a binomial variable is a matter of dispute.

In your case you are looking for a CI around a point estimate of 0.029.

A symmetric CI around such a point estimate is likely to include 0
and some negative values unless the sample size is very, very large.

Some people just truncate the interval at 0, but a more defensible
procedure is to work on a transformed scale and back-transform, or do
something approximately equivalent that yields positive endpoints
for the CI with about the right coverage. [R] ci has several pointers
to the literature.

Alternative CIs can be got in this way:

. gen rep78_1 = rep78 == 1
. ci rep78_1 if rep78 < ., binomial jeffreys
. ci rep78_1 if rep78 < ., binomial Wilson

Nick
n.j.cox@durham.ac.uk

Martin Weiss

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...

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```