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st: RE: Confidence Interval for Proportion

From   "Nick Cox" <>
To   <>
Subject   st: RE: Confidence Interval for Proportion
Date   Tue, 11 Mar 2008 14:05:04 -0000

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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