<?xml version="1.0" encoding="utf-8"?><!DOCTYPE article  PUBLIC '-//OASIS//DTD DocBook XML V4.4//EN'  'http://www.docbook.org/xml/4.4/docbookx.dtd'><article><articleinfo><title>FAQ/BinomialConfidence/2gpp</title><revhistory><revision><revnumber>10</revnumber><date>2013-03-08 10:17:37</date><authorinitials>localhost</authorinitials><revremark>converted to 1.6 markup</revremark></revision><revision><revnumber>9</revnumber><date>2012-06-25 14:01:53</date><authorinitials>PeterWatson</authorinitials></revision><revision><revnumber>8</revnumber><date>2010-08-27 09:21:23</date><authorinitials>PeterWatson</authorinitials></revision><revision><revnumber>7</revnumber><date>2010-08-26 15:50:41</date><authorinitials>PeterWatson</authorinitials></revision><revision><revnumber>6</revnumber><date>2010-08-26 15:49:57</date><authorinitials>PeterWatson</authorinitials></revision><revision><revnumber>5</revnumber><date>2010-08-26 15:28:28</date><authorinitials>PeterWatson</authorinitials></revision><revision><revnumber>4</revnumber><date>2010-08-26 15:28:00</date><authorinitials>PeterWatson</authorinitials></revision><revision><revnumber>3</revnumber><date>2010-08-26 14:14:38</date><authorinitials>PeterWatson</authorinitials></revision><revision><revnumber>2</revnumber><date>2010-08-26 09:11:30</date><authorinitials>PeterWatson</authorinitials></revision><revision><revnumber>1</revnumber><date>2010-08-26 09:11:21</date><authorinitials>PeterWatson</authorinitials></revision></revhistory></articleinfo><section><title>Confidence interval for paired binomial proportions</title><para><ulink url="https://lsr-wiki-02.mrc-cbu.cam.ac.uk/statswiki/FAQ/BinomialConfidence/2gpp/statswiki/McNemar#">McNemar</ulink>'s test is commonly used to test whether two correlated proportions differ. Unfortunately this test does not tprovide a confidence interval for the difference in proportions.  </para><para>The classical Wald statistic which is used for constructing confidence intervals for proportions produces too narrow a confidence interval when the difference in proportions is close to zero or one (Newcombe (1998)). Newcombe, instead, suggests using a modification of Wilson's (1927) method based on a single proportion. Agresti &amp; Kin (2005) also find Wilson's method produces good coverage and also suggest an improved confidence interval may be obtained by a simple modification of the Wald statistic. These are all included in this EXCEL <ulink url="https://lsr-wiki-02.mrc-cbu.cam.ac.uk/statswiki/FAQ/BinomialConfidence/2gpp/statswiki/FAQ/BinomialConfidence/2gpp?action=AttachFile&amp;do=get&amp;target=paired_pci.xls">spreadsheet.</ulink>  </para><itemizedlist><listitem><para><ulink url="https://lsr-wiki-02.mrc-cbu.cam.ac.uk/statswiki/FAQ/BinomialConfidence/2gpp/statswiki/FAQ/BinomialCofidence/2gpp/Rcode#">Some R code for the Agresti-Min approach above is also available</ulink> </para></listitem></itemizedlist><para><emphasis role="underline">References</emphasis> </para><para><ulink url="https://lsr-wiki-02.mrc-cbu.cam.ac.uk/statswiki/FAQ/BinomialConfidence/2gpp/statswiki/FAQ/BinomialConfidence/2gpp?action=AttachFile&amp;do=get&amp;target=agresti.pdf">Agresti A and Min Y (2005) Simple improved confidence intervals for comparing matched proportions.</ulink> <emphasis>Statistics in Medicine</emphasis> <emphasis role="strong">24(5)</emphasis> 729-740. </para><para>Newcombe RG (1998) Improved confidence intervals for the difference between binomial proportions based on paired data. <emphasis>Statistics in Medicine</emphasis> <emphasis role="strong">17</emphasis> 2635-2650.  </para><para>Lee S &amp; Lee S-C (2007) An improved confidence interval for the population proportion in a double sampling scheme subject to false-positive misclassification, <emphasis>Journal of the Korean Statistical Society</emphasis> <emphasis role="strong">36</emphasis> 275–284. (reference for agrestic-oull method used in above spreadsheet). </para></section></article>