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: [email protected]
[mailto:[email protected]] On Behalf Of Roger Newson
Sent: Friday, March 19, 2004 11:08 AM
To: [email protected]
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: [email protected]
Website: http://www.kcl-phs.org.uk/rogernewson
Opinions expressed are those of the author, not the institution.
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