    # Re: st: CC exact 95% confidence interval brackets 1 while the P value is < .05

 From Mike Lacy To statalist@hsphsun2.harvard.edu Subject Re: st: CC exact 95% confidence interval brackets 1 while the P value is < .05 Date Thu, 28 Sep 2006 07:42:23 -0600

Date: Wed, 27 Sep 2006 13:15:22 -0700
From: Bill Warburton <bill.warburton@ubc.ca>
Subject: st: CC exact 95% confidence interval brackets 1 while the P value is < .05

Can you tell me why the exact 95% confidence interval brackets 1 while the P
value is < .05?

In a logistic regression I was suspicious of the rather narrow confidence
intervals in the analysis of a relatively rare event so I checked using a
2x2 table with an exact test (results below) and the exact confidence
interval does indeed bracket 1, but the p-value given is less than .05(?).

Can you tell me how to interpret/report this?
The distribution of a statistic assuming the null to be true, which is used to obtain a p-value, is not the same as the distribution of a statistic when the null is not assumed to be true, as is the case for a confidence interval. The formulae for ordinary asymptotic tests for means, for example, obscure this fact, but a simple demonstration of the principle can be seen in the formula for the standard error for the test on a single proportion, vs. the standard error expression in the formula for a confidence interval on a proportion: The form is the same, but one formula uses an assumed null value, while the other uses an observed value, which are in general quite different. The practice of using confidence intervals as a closet hypothesis test is essentially a trick that happens to work only with statistics for which the distribution is the same whether or not the null is true. The resolution of the chimerical contradiction, then, is to not intepret your CI as though it were a slightly disguised hypothesis test. It rests on a different logic and answers a different question.

Sincerely,

=-=-=-=-=-=-=-=-=-=-=-=-=
Mike Lacy
Fort Collins CO USA
(970) 491-6721 office

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