<?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/Power</title><revhistory><revision><revnumber>30</revnumber><date>2014-03-27 12:23:21</date><authorinitials>PeterWatson</authorinitials></revision><revision><revnumber>29</revnumber><date>2013-03-08 10:17:27</date><authorinitials>localhost</authorinitials><revremark>converted to 1.6 markup</revremark></revision><revision><revnumber>28</revnumber><date>2007-09-28 09:01:56</date><authorinitials>PeterWatson</authorinitials></revision><revision><revnumber>27</revnumber><date>2007-09-28 08:58:44</date><authorinitials>PeterWatson</authorinitials></revision><revision><revnumber>26</revnumber><date>2007-09-28 08:57:07</date><authorinitials>PeterWatson</authorinitials></revision><revision><revnumber>25</revnumber><date>2007-09-28 08:56:43</date><authorinitials>PeterWatson</authorinitials></revision><revision><revnumber>24</revnumber><date>2007-07-23 14:14:47</date><authorinitials>PeterWatson</authorinitials></revision><revision><revnumber>23</revnumber><date>2007-07-23 14:14:13</date><authorinitials>PeterWatson</authorinitials></revision><revision><revnumber>22</revnumber><date>2007-07-23 14:13:32</date><authorinitials>PeterWatson</authorinitials></revision><revision><revnumber>21</revnumber><date>2007-07-23 14:10:30</date><authorinitials>PeterWatson</authorinitials></revision><revision><revnumber>20</revnumber><date>2007-07-23 14:06:26</date><authorinitials>PeterWatson</authorinitials></revision><revision><revnumber>19</revnumber><date>2007-07-23 14:06:01</date><authorinitials>PeterWatson</authorinitials></revision><revision><revnumber>18</revnumber><date>2007-07-23 14:04:54</date><authorinitials>PeterWatson</authorinitials></revision><revision><revnumber>17</revnumber><date>2007-07-23 14:03:57</date><authorinitials>PeterWatson</authorinitials></revision><revision><revnumber>16</revnumber><date>2006-07-12 16:00:38</date><authorinitials>pc0082.mrc-cbu.cam.ac.uk</authorinitials></revision><revision><revnumber>15</revnumber><date>2006-07-12 15:59:56</date><authorinitials>pc0082.mrc-cbu.cam.ac.uk</authorinitials></revision><revision><revnumber>14</revnumber><date>2006-07-12 15:59:21</date><authorinitials>pc0082.mrc-cbu.cam.ac.uk</authorinitials></revision><revision><revnumber>13</revnumber><date>2006-07-12 15:57:46</date><authorinitials>pc0082.mrc-cbu.cam.ac.uk</authorinitials></revision><revision><revnumber>12</revnumber><date>2006-07-12 15:57:17</date><authorinitials>pc0082.mrc-cbu.cam.ac.uk</authorinitials></revision><revision><revnumber>11</revnumber><date>2006-07-12 15:50:22</date><authorinitials>pc0082.mrc-cbu.cam.ac.uk</authorinitials></revision><revision><revnumber>10</revnumber><date>2006-07-12 15:47:25</date><authorinitials>pc0082.mrc-cbu.cam.ac.uk</authorinitials></revision><revision><revnumber>9</revnumber><date>2006-07-12 15:38:10</date><authorinitials>pc0082.mrc-cbu.cam.ac.uk</authorinitials></revision><revision><revnumber>8</revnumber><date>2006-07-12 15:37:03</date><authorinitials>pc0082.mrc-cbu.cam.ac.uk</authorinitials></revision><revision><revnumber>7</revnumber><date>2006-07-12 15:34:51</date><authorinitials>pc0082.mrc-cbu.cam.ac.uk</authorinitials></revision><revision><revnumber>6</revnumber><date>2006-07-12 15:34:11</date><authorinitials>pc0082.mrc-cbu.cam.ac.uk</authorinitials></revision><revision><revnumber>5</revnumber><date>2006-07-12 15:33:36</date><authorinitials>pc0082.mrc-cbu.cam.ac.uk</authorinitials></revision><revision><revnumber>4</revnumber><date>2006-07-12 15:30:11</date><authorinitials>pc0082.mrc-cbu.cam.ac.uk</authorinitials></revision><revision><revnumber>3</revnumber><date>2006-07-12 15:22:19</date><authorinitials>pc0082.mrc-cbu.cam.ac.uk</authorinitials></revision><revision><revnumber>2</revnumber><date>2006-07-12 15:19:45</date><authorinitials>pc0082.mrc-cbu.cam.ac.uk</authorinitials></revision><revision><revnumber>1</revnumber><date>2006-07-12 15:16:49</date><authorinitials>pc0082.mrc-cbu.cam.ac.uk</authorinitials></revision></revhistory></articleinfo><para><emphasis role="strong">Table of sample sizes required for tests of non-zero Kendall, Spearman and Pearson correlations</emphasis> </para><para>We assume 90% power and a Type I error of 5% </para><para>Null hypothesis : correlation = 0; </para><para>Alternative: correlation = non-zero value </para><para>If you know the sign of the non-zero correlation the test is one-tailed otherwise it is two-tailed. </para><para>Computations using methods in Kraemer, HC &amp; Thiemann, S (1987) How Many Subjects? Statistical Power Analysis in Research. Sage:London. </para><itemizedlist><listitem><para><ulink url="https://lsr-wiki-01.mrc-cbu.cam.ac.uk/statswiki/FAQ/Power/statswiki/FAQ/powprogs#">Power calculator also available</ulink> for the Pearson correlation. </para></listitem><listitem><para>Dunlap WP and Myers L (1997) show that for a Pearson correlation, r, 8/$$r^text{2}$$ gives a total sample size with at least 80% power. </para></listitem></itemizedlist><para>Correlations of 0.1, 0.3 and 0.5 correspond to small, medium and high correlations using <ulink url="https://lsr-wiki-01.mrc-cbu.cam.ac.uk/statswiki/FAQ/Power/statswiki/FAQ/effectSize#">rules of thumb.</ulink> </para><informaltable><tgroup cols="13"><colspec colname="col_0" colwidth="14*"/><colspec colname="col_1"/><colspec colname="col_2"/><colspec colname="col_3"/><colspec colname="col_4"/><colspec colname="col_5"/><colspec colname="col_6"/><colspec colname="col_7"/><colspec colname="col_8"/><colspec colname="col_9"/><colspec colname="col_10"/><colspec colname="col_11"/><colspec colname="col_12"/><tbody><row rowsep="1"><entry colsep="1" nameend="col_6" namest="col_0" rowsep="1"/><entry colsep="1" nameend="col_9" namest="col_7" rowsep="1"><para>1-tail </para></entry><entry colsep="1" nameend="col_12" namest="col_10" rowsep="1"><para>2-tail </para></entry></row><row rowsep="1"><entry colsep="1" nameend="col_6" namest="col_0" rowsep="1"><para>correlation </para></entry><entry colsep="1" rowsep="1"><para>Kendall </para></entry><entry colsep="1" rowsep="1"><para>Spearman </para></entry><entry colsep="1" rowsep="1"><para>Pearson </para></entry><entry colsep="1" rowsep="1"><para>Kendall </para></entry><entry colsep="1" rowsep="1"><para>Spearman </para></entry><entry colsep="1" rowsep="1"><para>Pearson </para></entry></row><row rowsep="1"><entry colsep="1" nameend="col_6" namest="col_0" rowsep="1"><para><emphasis role="strong">0.1</emphasis> </para></entry><entry colsep="1" rowsep="1"><para><emphasis role="strong">1041</emphasis> </para></entry><entry colsep="1" rowsep="1"><para><emphasis role="strong">1013</emphasis> </para></entry><entry colsep="1" rowsep="1"><para><emphasis role="strong">854</emphasis> </para></entry><entry colsep="1" rowsep="1"><para><emphasis role="strong">1277</emphasis> </para></entry><entry colsep="1" rowsep="1"><para><emphasis role="strong">1111</emphasis> </para></entry><entry colsep="1" rowsep="1"><para><emphasis role="strong">1047</emphasis> </para></entry></row><row rowsep="1"><entry colsep="1" nameend="col_6" namest="col_0" rowsep="1"><para>0.2 </para></entry><entry colsep="1" rowsep="1"><para>224 </para></entry><entry colsep="1" rowsep="1"><para>250 </para></entry><entry colsep="1" rowsep="1"><para>212 </para></entry><entry colsep="1" rowsep="1"><para>274 </para></entry><entry colsep="1" rowsep="1"><para>307 </para></entry><entry colsep="1" rowsep="1"><para>259 </para></entry></row><row rowsep="1"><entry colsep="1" nameend="col_6" namest="col_0" rowsep="1"><para><emphasis role="strong">0.3</emphasis> </para></entry><entry colsep="1" rowsep="1"><para><emphasis role="strong">106</emphasis> </para></entry><entry colsep="1" rowsep="1"><para><emphasis role="strong">107</emphasis> </para></entry><entry colsep="1" rowsep="1"><para><emphasis role="strong">93</emphasis> </para></entry><entry colsep="1" rowsep="1"><para><emphasis role="strong">129</emphasis> </para></entry><entry colsep="1" rowsep="1"><para><emphasis role="strong">130</emphasis> </para></entry><entry colsep="1" rowsep="1"><para><emphasis role="strong">113</emphasis> </para></entry></row><row rowsep="1"><entry colsep="1" nameend="col_6" namest="col_0" rowsep="1"><para>0.4 </para></entry><entry colsep="1" rowsep="1"><para>58 </para></entry><entry colsep="1" rowsep="1"><para>62 </para></entry><entry colsep="1" rowsep="1"><para>51 </para></entry><entry colsep="1" rowsep="1"><para>70 </para></entry><entry colsep="1" rowsep="1"><para>75 </para></entry><entry colsep="1" rowsep="1"><para>62 </para></entry></row><row rowsep="1"><entry colsep="1" nameend="col_6" namest="col_0" rowsep="1"><para><emphasis role="strong">0.5</emphasis> </para></entry><entry colsep="1" rowsep="1"><para><emphasis role="strong">37</emphasis> </para></entry><entry colsep="1" rowsep="1"><para><emphasis role="strong">39</emphasis> </para></entry><entry colsep="1" rowsep="1"><para><emphasis role="strong">32</emphasis> </para></entry><entry colsep="1" rowsep="1"><para><emphasis role="strong">44</emphasis> </para></entry><entry colsep="1" rowsep="1"><para><emphasis role="strong">46</emphasis> </para></entry><entry colsep="1" rowsep="1"><para><emphasis role="strong">38</emphasis> </para></entry></row><row rowsep="1"><entry colsep="1" nameend="col_6" namest="col_0" rowsep="1"><para>0.6 </para></entry><entry colsep="1" rowsep="1"><para>25 </para></entry><entry colsep="1" rowsep="1"><para>26 </para></entry><entry colsep="1" rowsep="1"><para>21 </para></entry><entry colsep="1" rowsep="1"><para>29 </para></entry><entry colsep="1" rowsep="1"><para>30 </para></entry><entry colsep="1" rowsep="1"><para>25 </para></entry></row><row rowsep="1"><entry colsep="1" nameend="col_6" namest="col_0" rowsep="1"><para>0.7 </para></entry><entry colsep="1" rowsep="1"><para>18 </para></entry><entry colsep="1" rowsep="1"><para>19 </para></entry><entry colsep="1" rowsep="1"><para>15 </para></entry><entry colsep="1" rowsep="1"><para>21 </para></entry><entry colsep="1" rowsep="1"><para>21 </para></entry><entry colsep="1" rowsep="1"><para>17 </para></entry></row><row rowsep="1"><entry colsep="1" nameend="col_6" namest="col_0" rowsep="1"><para>0.8 </para></entry><entry colsep="1" rowsep="1"><para>13 </para></entry><entry colsep="1" rowsep="1"><para>&lt;14 </para></entry><entry colsep="1" rowsep="1"><para>&lt;10 </para></entry><entry colsep="1" rowsep="1"><para>15 </para></entry><entry colsep="1" rowsep="1"><para>15 </para></entry><entry colsep="1" rowsep="1"><para>12 </para></entry></row><row rowsep="1"><entry colsep="1" nameend="col_6" namest="col_0" rowsep="1"><para>0.9 </para></entry><entry colsep="1" rowsep="1"><para>9 </para></entry><entry colsep="1" rowsep="1"><para>&lt;10 </para></entry><entry colsep="1" rowsep="1"><para>&lt;10 </para></entry><entry colsep="1" rowsep="1"><para>11 </para></entry><entry colsep="1" rowsep="1"><para>11 </para></entry><entry colsep="1" rowsep="1"><para>&lt;10 </para></entry></row></tbody></tgroup></informaltable><para><emphasis role="underline">Reference</emphasis> </para><para>Dunlap WP and Myers L (1997) Approximating Power for significance tests with one degree of freedom. <emphasis>Psychological Methods</emphasis> <emphasis role="strong">2(2)</emphasis> 186-191. </para></article>