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RE: st:Confidence interval of difference between two proportions and -csi-

From   Roger Newson <>
Subject   RE: st:Confidence interval of difference between two proportions and -csi-
Date   Fri, 19 Mar 2004 17:08:01 +0000

At 09:08 19/03/04 -0600, Bill Dupont wrote:

Non-rejection definition:

A 95% confidence interval, (L, U), consists of all values of theta that
can not be rejected at the 5% significance level given the data.
An exact confidence region defined in that way will not always be an interval if the test statistic is based on a discrete random variable, eg in the case of Fisher's exact test, because there may be "holes" in the non-rejection region, caused by the fact that the P-value can only take finitely many values (or maybe countably infinitely many values as in the Poisson case). The conservative confidence intervals defined by Clopper-Pearson, Mehta-Patel-Gray etc. include the holes, and are not exact either in the coverage sense or in the non-rejection sense, although they are conservative in the coverage sense. However, they are exact in that they use the exact discrete distribution of the test statistic, instead of a continuous approximation.


Roger Newson
Lecturer in Medical Statistics
Department of Public Health Sciences
King's College London
5th Floor, Capital House
42 Weston Street
London SE1 3QD
United Kingdom

Tel: 020 7848 6648 International +44 20 7848 6648
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Opinions expressed are those of the author, not the institution.

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