<?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/2gp</title><revhistory><revision><revnumber>7</revnumber><date>2013-03-08 10:17:36</date><authorinitials>localhost</authorinitials><revremark>converted to 1.6 markup</revremark></revision><revision><revnumber>6</revnumber><date>2010-08-27 11:19:41</date><authorinitials>PeterWatson</authorinitials></revision><revision><revnumber>5</revnumber><date>2010-08-27 09:26:54</date><authorinitials>PeterWatson</authorinitials></revision><revision><revnumber>4</revnumber><date>2010-08-25 16:00:00</date><authorinitials>PeterWatson</authorinitials></revision><revision><revnumber>3</revnumber><date>2010-08-25 15:59:27</date><authorinitials>PeterWatson</authorinitials></revision><revision><revnumber>2</revnumber><date>2010-08-25 15:56:35</date><authorinitials>PeterWatson</authorinitials></revision><revision><revnumber>1</revnumber><date>2010-08-25 15:56:28</date><authorinitials>PeterWatson</authorinitials></revision></revhistory></articleinfo><section><title>Improved confidence limits for comparing two independent binomial proportions</title><para>The two-sample chi-square test (e.g. CROSSTABS in SPSS) can be used to test statistical significance of the difference in two independent proportions but this test does not provide a confidence interval on the magnitude of this difference. </para><para>Newcombe (1998) further goes on to compare various methods for giving confidence intervals for the difference in a pair of proportions from two different groups. he concludes that the Wald confidence interval is biased when the difference in proportions is close to zero or (+/-) one. As for a single proportion he recommends the two-sample analogue of the Wilson one-sample confidence interval. </para><para>This EXCEL <ulink url="https://lsr-wiki-02.mrc-cbu.cam.ac.uk/statswiki/FAQ/BinomialConfidence/2gp/statswiki/FAQ/BinomialConfidence/2gp?action=AttachFile&amp;do=get&amp;target=bin2.xls">spreadsheet</ulink> computes the two sample analogues of the methods in the one-sample spreadsheet.  </para><para><emphasis role="underline">References</emphasis> </para><para>Moore DS &amp; <ulink url="https://lsr-wiki-02.mrc-cbu.cam.ac.uk/statswiki/FAQ/BinomialConfidence/2gp/statswiki/McCabe#">McCabe</ulink> GP (2006) Introduction to the practice of statistics (5th ed.). WH Freeman:New York. (This mentions the two sample analogue of the Agresti-Coull method which was not mentioned in the original paper which dealt with the one-sample case). </para><para>Newcombe RG (1998) Interval estimation for the difference between independent proportions: comparison of eleven methods. <emphasis>Statistics in Medicine</emphasis> <emphasis role="strong">17</emphasis> 873-890. </para></section></article>