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

From   "Dupont, William" <>
To   <>
Subject   RE: st:Confidence interval of difference between two proportions and -csi-
Date   Fri, 19 Mar 2004 11:19:30 -0600

Unfortunately, the harder one looks at frequentist based inference, the
more difficult and fragile it appears.  Its enough to drive one to


-----Original Message-----
[] On Behalf Of Roger Newson
Sent: Friday, March 19, 2004 11:08 AM
Subject: RE: st:Confidence interval of difference between two
proportions and -csi-

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,
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
Poisson case). The conservative confidence intervals defined by 
Clopper-Pearson, Mehta-Patel-Gray etc. include the holes, and are not
either in the coverage sense or in the non-rejection sense, although
are conservative in the coverage sense. However, they are exact in that 
they use the exact discrete distribution of the test statistic, instead
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
Fax: 020 7848 6620 International +44 20 7848 6620
   or 020 7848 6605 International +44 20 7848 6605

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

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