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st: RE: RE: RE: Confidence Interval for Proportion

From   "Newson, Roger B" <>
To   <>
Subject   st: RE: RE: RE: Confidence Interval for Proportion
Date   Tue, 11 Mar 2008 17:02:19 -0000

Coverage using the -exact- option is not really exact, but conservative.
The -exact- option is so called because it uses the exact distribution
of the sample proportion value, under each population proportion value,
to calculate confidence limits whose coverage probability is (if
anything) conservative. 


Roger B Newson
Lecturer in Medical Statistics
Respiratory Epidemiology and Public Health Group
National Heart and Lung Institute
Imperial College London
Royal Brompton campus
Room 33, Emmanuel Kaye Building
1B Manresa Road
London SW3 6LR
Tel: +44 (0)20 7352 8121 ext 3381
Fax: +44 (0)20 7351 8322
Web page:
Departmental Web page:

Opinions expressed are those of the author, not of the institution.

-----Original Message-----
[] On Behalf Of Lachenbruch,
Sent: 11 March 2008 16:42
Subject: st: RE: RE: Confidence Interval for Proportion

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).


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

-----Original Message-----
[] On Behalf Of Nick Cox
Sent: Tuesday, March 11, 2008 7:05 AM
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


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
in the repair record? Something`s wrong with the standard error, I do
know what, though...

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