# RE: st: RE: Confidence Interval for Proportion

 From "Nick Cox" To Subject RE: st: RE: Confidence Interval for Proportion Date Tue, 11 Mar 2008 14:40:16 -0000

```Very good point.

Maarten buis

Though I could not find in the paper documentation which method is used
by -proportion-. Moreover, here we are dealing with a multinomial
proportions, which is subject to a (obviously related) debate about
properties of the different simultaneous confidence intervals. An
overview can be found in (Hou, et al 2003).

Chia-Ding Hou, Jengtung Chiang and John Jen Tai (2003) `A family of
simultaneous confidence intervals for multinomial proportions',
Computational Statistics & Data Analysis, 43(1): 29--45.

--- Nick Cox <n.j.cox@durham.ac.uk> wrote:

> 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
> "1"
> in the repair record? Something`s wrong with the standard error, I do
> not
> know what, though...

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