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From |
"Newson, Roger B" <r.newson@imperial.ac.uk> |

To |
<statalist@hsphsun2.harvard.edu> |

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 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 UNITED KINGDOM Tel: +44 (0)20 7352 8121 ext 3381 Fax: +44 (0)20 7351 8322 Email: r.newson@imperial.ac.uk Web page: www.imperial.ac.uk/nhli/r.newson/ Departmental Web page: http://www1.imperial.ac.uk/medicine/about/divisions/nhli/respiration/pop genetics/reph/ Opinions expressed are those of the author, not of the institution. -----Original Message----- From: owner-statalist@hsphsun2.harvard.edu [mailto:owner-statalist@hsphsun2.harvard.edu] On Behalf Of Lachenbruch, Peter Sent: 11 March 2008 16:42 To: statalist@hsphsun2.harvard.edu 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). 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... * * For searches and help try: * http://www.stata.com/support/faqs/res/findit.html * http://www.stata.com/support/statalist/faq * http://www.ats.ucla.edu/stat/stata/ * * For searches and help try: * http://www.stata.com/support/faqs/res/findit.html * http://www.stata.com/support/statalist/faq * http://www.ats.ucla.edu/stat/stata/ * * For searches and help try: * http://www.stata.com/support/faqs/res/findit.html * http://www.stata.com/support/statalist/faq * http://www.ats.ucla.edu/stat/stata/

**References**:**st: Confidence Interval for Proportion***From:*"Martin Weiss" <martin.weiss@uni-tuebingen.de>

**st: RE: Confidence Interval for Proportion***From:*"Nick Cox" <n.j.cox@durham.ac.uk>

**st: RE: RE: Confidence Interval for Proportion***From:*"Lachenbruch, Peter" <Peter.Lachenbruch@oregonstate.edu>

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