<?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/oddsr</title><revhistory><revision><revnumber>24</revnumber><date>2015-11-12 15:36:24</date><authorinitials>PeterWatson</authorinitials></revision><revision><revnumber>23</revnumber><date>2013-03-08 10:17:19</date><authorinitials>localhost</authorinitials><revremark>converted to 1.6 markup</revremark></revision><revision><revnumber>22</revnumber><date>2011-08-10 08:59:21</date><authorinitials>PeterWatson</authorinitials></revision><revision><revnumber>21</revnumber><date>2010-11-24 12:56:11</date><authorinitials>PeterWatson</authorinitials></revision><revision><revnumber>20</revnumber><date>2010-11-24 12:55:48</date><authorinitials>PeterWatson</authorinitials></revision><revision><revnumber>19</revnumber><date>2007-01-25 16:04:30</date><authorinitials>PeterWatson</authorinitials></revision><revision><revnumber>18</revnumber><date>2007-01-15 10:12:45</date><authorinitials>PeterWatson</authorinitials></revision><revision><revnumber>17</revnumber><date>2006-12-06 13:16:55</date><authorinitials>PeterWatson</authorinitials></revision><revision><revnumber>16</revnumber><date>2006-12-06 13:16:34</date><authorinitials>PeterWatson</authorinitials></revision><revision><revnumber>15</revnumber><date>2006-11-16 14:16:51</date><authorinitials>PeterWatson</authorinitials></revision><revision><revnumber>14</revnumber><date>2006-11-16 14:15:57</date><authorinitials>PeterWatson</authorinitials></revision><revision><revnumber>13</revnumber><date>2006-11-16 14:14:06</date><authorinitials>PeterWatson</authorinitials></revision><revision><revnumber>12</revnumber><date>2006-11-16 14:11:51</date><authorinitials>PeterWatson</authorinitials></revision><revision><revnumber>11</revnumber><date>2006-11-15 12:31:50</date><authorinitials>PeterWatson</authorinitials></revision><revision><revnumber>10</revnumber><date>2006-11-14 17:23:33</date><authorinitials>PeterWatson</authorinitials></revision><revision><revnumber>9</revnumber><date>2006-11-14 17:22:14</date><authorinitials>PeterWatson</authorinitials></revision><revision><revnumber>8</revnumber><date>2006-11-14 17:21:29</date><authorinitials>PeterWatson</authorinitials></revision><revision><revnumber>7</revnumber><date>2006-11-14 17:20:38</date><authorinitials>PeterWatson</authorinitials></revision><revision><revnumber>6</revnumber><date>2006-11-14 17:18:50</date><authorinitials>PeterWatson</authorinitials></revision><revision><revnumber>5</revnumber><date>2006-11-14 17:17:38</date><authorinitials>PeterWatson</authorinitials></revision><revision><revnumber>4</revnumber><date>2006-11-14 17:14:07</date><authorinitials>PeterWatson</authorinitials></revision><revision><revnumber>3</revnumber><date>2006-11-14 17:13:43</date><authorinitials>PeterWatson</authorinitials></revision><revision><revnumber>2</revnumber><date>2006-11-14 17:13:03</date><authorinitials>PeterWatson</authorinitials></revision><revision><revnumber>1</revnumber><date>2006-11-14 17:10:06</date><authorinitials>PeterWatson</authorinitials></revision></revhistory></articleinfo><section><title>Testing an odds ratio</title><para>Suppose we have a 2 x 2 table of frequencies  </para><informaltable><tgroup cols="5"><colspec colname="col_0" colwidth="33*"/><colspec colname="col_1"/><colspec colname="col_2"/><colspec colname="col_3" colwidth="33*"/><colspec colname="col_4" colwidth="34*"/><tbody><row rowsep="1"><entry colsep="1" nameend="col_2" namest="col_0" rowsep="1"/><entry colsep="1" rowsep="1"><para> <emphasis role="strong">Col 1</emphasis> </para></entry><entry colsep="1" rowsep="1"><para> <emphasis role="strong">Col 2</emphasis></para></entry></row><row rowsep="1"><entry align="center" colsep="1" nameend="col_2" namest="col_0" rowsep="1"><para> <emphasis role="strong">Row 1</emphasis> </para></entry><entry colsep="1" rowsep="1"><para> a </para></entry><entry colsep="1" rowsep="1"><para> b </para></entry></row><row rowsep="1"><entry align="center" colsep="1" nameend="col_2" namest="col_0" rowsep="1"><para> <emphasis role="strong">Row 2</emphasis> </para></entry><entry colsep="1" rowsep="1"><para> c </para></entry><entry colsep="1" rowsep="1"><para> d </para></entry></row></tbody></tgroup></informaltable><para>The Odds Ratio is defined as ad/bc </para><para>It turns out that  </para><screen><![CDATA[Variance{ln(OR)} = (1/a) + (1/b) + (1/c) + (1/d)]]></screen><para>so it follows </para><para>ln(OR)*ln(OR) /  variance ( ln(OR) ) </para><para>is chi-square on 1 degree of freedom. </para><para>If you have a zero cell then adding one half to all the frequencies enables an estimate of the odds ratio to be made. </para><para>An odds ratio test is carried out by this <ulink url="https://imaging.mrc-cbu.cam.ac.uk/statswiki/FAQ/oddsr/statswiki/FAQ/oddsr?action=AttachFile&amp;do=get&amp;target=oratio.xls">spreadsheet</ulink>. Bonett and Price Jnr (2015) report on an inproved form of standard error for the Odds Ratio. </para><para><emphasis role="underline">References</emphasis> </para><para>Agresti A (1996) An Introduction to Categorical Data Analysis. Wiley:New York. </para><para>Bonett DG and Price Jr RM (2015) Varying coefficient meta-analysis methods for odds ratios and risk ratios. <emphasis>Psychological Methods</emphasis> <emphasis role="strong">20(3)</emphasis> 394-406. </para><para>Everitt BS (1996) Making Sense of Statistics in Psychology A Second Level Course. OUP:Oxford.  </para><para>Hosmer DW and Lemeshow S (1995) Applied Logistic Regression. 2nd Edition. Wiley:New York. In CBSU library. A 3rd edition is due to be published in 2013.  </para></section></article>