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From |
"Dupont, William" <william.dupont@vanderbilt.edu> |

To |
<statalist@hsphsun2.harvard.edu> |

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

Date |
Fri, 19 Mar 2004 09:08:39 -0600 |

Statalisters I believe that there is some confusion about the meaning of exact confidence intervals. Confidence intervals are defined in two ways. Let theta be a parameter and L U be two statistics. Then confidence intervals are defined as follows: Coverage definition: (L, U) is a 95% confidence interval for theta if Pr[L < theta < U] = 0.95 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. These two definitions are equivalent for normally distributed data in which the mean and variance are unrelated. In epidemiology and other disciplines we often work with statistics (e.g. odds ratios) in which these definitions yield different intervals. Exact confidence intervals use the non-rejection definition. When estimating odds ratios from 2x2 tables, the total number of successes in both groups is close to being an ancillary statistic in the sense that knowing this total tells us nothing about the true odds ratio. The Conditionality Principle requires that we condition our inferences on ancillary statistics. It is for this reason that we condition on the marginal totals of a 2x2 table when making inferences about odds ratios. If you accept the conditionality argument then the usual exact confidence interval is correctly derived from the hypergeometric distribution. It is an exact interval not because it uses the hypergeometric distribution but because it complies with the non-rejection definition given above. It should be noted that when these definitions disagree, the non-rejection confidence interval will have a higher coverage probability than the analogous interval obtained by the coverage definition. In this sense, it is a more conservative interval. See Rothman and Greenland (1998) for further details. Bill Dupont -----Original Message----- From: owner-statalist@hsphsun2.harvard.edu [mailto:owner-statalist@hsphsun2.harvard.edu] On Behalf Of Garry Anderson Sent: Friday, March 19, 2004 2:11 AM To: statalist@hsphsun2.harvard.edu Subject: Re: st:Confidence interval of difference between two proportions and -csi- ... > >then the so-called "exact" confidence interval is generated. (Note, >however, that this confidence interval is conservative, not exact. It is >called "exact" because it uses the exact hypergeometric distribution to >calculate conservative confidence limits.) > >I hope this helps. > >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. > >* >* For searches and help try: >* http://www.stata.com/support/faqs/res/findit.html >* http://www.stata.com/support/statalist/faq >* http://www.ats.ucla.edu/stat/stata/ * * For searches and help try: * http://www.stata.com/support/faqs/res/findit.html * http://www.stata.com/support/statalist/faq * http://www.ats.ucla.edu/stat/stata/ * * For searches and help try: * http://www.stata.com/support/faqs/res/findit.html * http://www.stata.com/support/statalist/faq * http://www.ats.ucla.edu/stat/stata/

**Follow-Ups**:**RE: st:Confidence interval of difference between two proportions and -csi-***From:*Roger Newson <roger.newson@kcl.ac.uk>

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