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


From   "Nick Cox" <n.j.cox@durham.ac.uk>
To   <statalist@hsphsun2.harvard.edu>
Subject   RE: st:Confidence interval of difference between two proportions and -csi-
Date   Fri, 19 Mar 2004 17:38:46 -0000

Frequentist vs Bayes could be a red herring here, or at least 
that's my prior belief. Quite often, procedures suggested from 
a Bayes viewpoint turn out to have a frequentist interpretation, 
and vice versa, so the practical answer is identical, just that 
the arm-waving varies. In particular, frequentists and Bayesians 
should all be able to agree that intervals should not stray 
outside [0,1] (I hope). 

Thus the Jeffreys procedure for binomial confidence intervals 
is a continuity-corrected version of Clopper-Pearson. Dyed-in-the-wool 
frequentists can forget all about the prior distribution in the 
original. 

See also e.g. 

Donald B. Rubin. 1984. 
Bayesianly justifiable and relevant frequency calculations 
for the applied statistician. The Annals of Statistics 
12: 1151-1172.

Nick 
n.j.cox@durham.ac.uk 

> -----Original Message-----
> From: owner-statalist@hsphsun2.harvard.edu
> [mailto:owner-statalist@hsphsun2.harvard.edu]On Behalf Of Dupont,
> William
> Sent: 19 March 2004 17:20
> To: statalist@hsphsun2.harvard.edu
> Subject: RE: st:Confidence interval of difference between two
> proportions and -csi-
> 
> 
> Unfortunately, the harder one looks at frequentist based 
> inference, the
> more difficult and fragile it appears.  Its enough to drive one to
> Bayesianism!
> 
> Bill
> 
> -----Original Message-----
> From: owner-statalist@hsphsun2.harvard.edu
> [mailto:owner-statalist@hsphsun2.harvard.edu] On Behalf Of 
> Roger Newson
> Sent: Friday, March 19, 2004 11:08 AM
> To: statalist@hsphsun2.harvard.edu
> 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,
> 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
> 
> 
> --
> 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
> Email: roger.newson@kcl.ac.uk
> Website: http://www.kcl-phs.org.uk/rogernewson
> 
> Opinions expressed are those of the author, not the institution.
> 
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