<?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/PRsq</title><revhistory><revision><revnumber>5</revnumber><date>2013-03-08 10:17:14</date><authorinitials>localhost</authorinitials><revremark>converted to 1.6 markup</revremark></revision><revision><revnumber>4</revnumber><date>2010-07-22 12:06:09</date><authorinitials>PeterWatson</authorinitials></revision><revision><revnumber>3</revnumber><date>2010-07-22 11:36:05</date><authorinitials>PeterWatson</authorinitials></revision><revision><revnumber>2</revnumber><date>2010-07-22 10:11:22</date><authorinitials>PeterWatson</authorinitials></revision><revision><revnumber>1</revnumber><date>2010-07-22 10:10:54</date><authorinitials>PeterWatson</authorinitials></revision></revhistory></articleinfo><section><title>Sample sizes for selected values of R-squared and different numbers of groups in a one-way anova</title><para>The table below gives the total sample size required for 90% and 80% power for upto 8 groups in a one-way anova. In each case the type I error is taken as 5%. The rows in bold correspond to Cohen's rules of thumb for small, medium and large effect sizes. </para><informaltable><tgroup cols="25"><colspec colname="col_0"/><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"/><colspec colname="col_13"/><colspec colname="col_14"/><colspec colname="col_15"/><colspec colname="col_16"/><colspec colname="col_17"/><colspec colname="col_18"/><colspec colname="col_19"/><colspec colname="col_20"/><colspec colname="col_21"/><colspec colname="col_22"/><colspec colname="col_23"/><colspec colname="col_24"/><tbody><row rowsep="1"><entry colsep="1" nameend="col_12" namest="col_0" rowsep="1"/><entry colsep="1" nameend="col_18" namest="col_13" rowsep="1"><para>90% power </para></entry><entry colsep="1" nameend="col_24" namest="col_19" rowsep="1"><para>80% power </para></entry></row><row rowsep="1"><entry colsep="1" nameend="col_12" namest="col_0" rowsep="1"><para>R-squared </para></entry><entry colsep="1" rowsep="1"><para> K=3 </para></entry><entry colsep="1" rowsep="1"><para> K=4 </para></entry><entry colsep="1" rowsep="1"><para> K=5 </para></entry><entry colsep="1" rowsep="1"><para> K=6 </para></entry><entry colsep="1" rowsep="1"><para> K=7 </para></entry><entry colsep="1" rowsep="1"><para> K=8 </para></entry><entry colsep="1" rowsep="1"><para> K=3 </para></entry><entry colsep="1" rowsep="1"><para> K=4 </para></entry><entry colsep="1" rowsep="1"><para> K=5 </para></entry><entry colsep="1" rowsep="1"><para> K=6 </para></entry><entry colsep="1" rowsep="1"><para> K=7 </para></entry><entry colsep="1" rowsep="1"><para> K=8 </para></entry></row><row rowsep="1"><entry colsep="1" nameend="col_12" namest="col_0" rowsep="1"><para><emphasis role="strong">0.010</emphasis> </para></entry><entry colsep="1" rowsep="1"><para> <emphasis role="strong">1269</emphasis> </para></entry><entry colsep="1" rowsep="1"><para> <emphasis role="strong">1424</emphasis> </para></entry><entry colsep="1" rowsep="1"><para> <emphasis role="strong">1550</emphasis> </para></entry><entry colsep="1" rowsep="1"><para> <emphasis role="strong">1656</emphasis> </para></entry><entry colsep="1" rowsep="1"><para> <emphasis role="strong">1750</emphasis> </para></entry><entry colsep="1" rowsep="1"><para> <emphasis role="strong">1840</emphasis> </para></entry><entry colsep="1" rowsep="1"><para> <emphasis role="strong">969</emphasis> </para></entry><entry colsep="1" rowsep="1"><para> <emphasis role="strong">1096</emphasis> </para></entry><entry colsep="1" rowsep="1"><para> <emphasis role="strong">1200</emphasis> </para></entry><entry colsep="1" rowsep="1"><para> <emphasis role="strong">1290</emphasis> </para></entry><entry colsep="1" rowsep="1"><para> <emphasis role="strong">1372</emphasis> </para></entry><entry colsep="1" rowsep="1"><para> <emphasis role="strong">1448</emphasis> </para></entry></row><row rowsep="1"><entry colsep="1" nameend="col_12" namest="col_0" rowsep="1"><para><emphasis role="strong">0.059</emphasis> </para></entry><entry colsep="1" rowsep="1"><para> <emphasis role="strong">207</emphasis> </para></entry><entry colsep="1" rowsep="1"><para> <emphasis role="strong">232</emphasis> </para></entry><entry colsep="1" rowsep="1"><para> <emphasis role="strong">255</emphasis> </para></entry><entry colsep="1" rowsep="1"><para> <emphasis role="strong">270</emphasis> </para></entry><entry colsep="1" rowsep="1"><para> <emphasis role="strong">287</emphasis> </para></entry><entry colsep="1" rowsep="1"><para> <emphasis role="strong">304</emphasis> </para></entry><entry colsep="1" rowsep="1"><para> <emphasis role="strong">159</emphasis> </para></entry><entry colsep="1" rowsep="1"><para> <emphasis role="strong">180</emphasis> </para></entry><entry colsep="1" rowsep="1"><para> <emphasis role="strong">200</emphasis> </para></entry><entry colsep="1" rowsep="1"><para> <emphasis role="strong">216</emphasis> </para></entry><entry colsep="1" rowsep="1"><para> <emphasis role="strong">231</emphasis> </para></entry><entry colsep="1" rowsep="1"><para> <emphasis role="strong">240</emphasis> </para></entry></row><row rowsep="1"><entry colsep="1" nameend="col_12" namest="col_0" rowsep="1"><para> 0.10 </para></entry><entry colsep="1" rowsep="1"><para> 117 </para></entry><entry colsep="1" rowsep="1"><para> 132 </para></entry><entry colsep="1" rowsep="1"><para> 144 </para></entry><entry colsep="1" rowsep="1"><para> 154 </para></entry><entry colsep="1" rowsep="1"><para> 163 </para></entry><entry colsep="1" rowsep="1"><para> 172 </para></entry><entry colsep="1" rowsep="1"><para> 90 </para></entry><entry colsep="1" rowsep="1"><para> 103 </para></entry><entry colsep="1" rowsep="1"><para> 113 </para></entry><entry colsep="1" rowsep="1"><para> 122 </para></entry><entry colsep="1" rowsep="1"><para> 130 </para></entry><entry colsep="1" rowsep="1"><para> 137 </para></entry></row><row rowsep="1"><entry colsep="1" nameend="col_12" namest="col_0" rowsep="1"><para><emphasis role="strong">0.138</emphasis> </para></entry><entry colsep="1" rowsep="1"><para> <emphasis role="strong">84</emphasis> </para></entry><entry colsep="1" rowsep="1"><para> <emphasis role="strong">96</emphasis> </para></entry><entry colsep="1" rowsep="1"><para> <emphasis role="strong">105</emphasis> </para></entry><entry colsep="1" rowsep="1"><para> <emphasis role="strong">114</emphasis> </para></entry><entry colsep="1" rowsep="1"><para> <emphasis role="strong">119</emphasis> </para></entry><entry colsep="1" rowsep="1"><para> <emphasis role="strong">128</emphasis> </para></entry><entry colsep="1" rowsep="1"><para> <emphasis role="strong">66</emphasis> </para></entry><entry colsep="1" rowsep="1"><para> <emphasis role="strong">76</emphasis> </para></entry><entry colsep="1" rowsep="1"><para> <emphasis role="strong">80</emphasis> </para></entry><entry colsep="1" rowsep="1"><para> <emphasis role="strong">90</emphasis> </para></entry><entry colsep="1" rowsep="1"><para> <emphasis role="strong">98</emphasis> </para></entry><entry colsep="1" rowsep="1"><para> <emphasis role="strong">104</emphasis> </para></entry></row><row rowsep="1"><entry colsep="1" nameend="col_12" namest="col_0" rowsep="1"><para> 0.15 </para></entry><entry colsep="1" rowsep="1"><para> 76 </para></entry><entry colsep="1" rowsep="1"><para> 85 </para></entry><entry colsep="1" rowsep="1"><para> 93 </para></entry><entry colsep="1" rowsep="1"><para> 100 </para></entry><entry colsep="1" rowsep="1"><para> 106 </para></entry><entry colsep="1" rowsep="1"><para> 111 </para></entry><entry colsep="1" rowsep="1"><para>  58 </para></entry><entry colsep="1" rowsep="1"><para> 66 </para></entry><entry colsep="1" rowsep="1"><para> 73 </para></entry><entry colsep="1" rowsep="1"><para> 79 </para></entry><entry colsep="1" rowsep="1"><para> 84 </para></entry><entry colsep="1" rowsep="1"><para> 89 </para></entry></row><row rowsep="1"><entry colsep="1" nameend="col_12" namest="col_0" rowsep="1"><para> 0.20 </para></entry><entry colsep="1" rowsep="1"><para> 54 </para></entry><entry colsep="1" rowsep="1"><para> 61 </para></entry><entry colsep="1" rowsep="1"><para> 67 </para></entry><entry colsep="1" rowsep="1"><para> 72 </para></entry><entry colsep="1" rowsep="1"><para> 77 </para></entry><entry colsep="1" rowsep="1"><para> 81 </para></entry><entry colsep="1" rowsep="1"><para>  42 </para></entry><entry colsep="1" rowsep="1"><para> 49 </para></entry><entry colsep="1" rowsep="1"><para> 54 </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> 65 </para></entry></row><row rowsep="1"><entry colsep="1" nameend="col_12" namest="col_0" rowsep="1"><para> 0.25 </para></entry><entry colsep="1" rowsep="1"><para> 42 </para></entry><entry colsep="1" rowsep="1"><para> 47 </para></entry><entry colsep="1" rowsep="1"><para> 52 </para></entry><entry colsep="1" rowsep="1"><para> 56 </para></entry><entry colsep="1" rowsep="1"><para> 59 </para></entry><entry colsep="1" rowsep="1"><para> 63 </para></entry><entry colsep="1" rowsep="1"><para>  33 </para></entry><entry colsep="1" rowsep="1"><para> 38 </para></entry><entry colsep="1" rowsep="1"><para> 42 </para></entry><entry colsep="1" rowsep="1"><para> 45 </para></entry><entry colsep="1" rowsep="1"><para> 48 </para></entry><entry colsep="1" rowsep="1"><para> 51 </para></entry></row><row rowsep="1"><entry colsep="1" nameend="col_12" namest="col_0" rowsep="1"><para> 0.30 </para></entry><entry colsep="1" rowsep="1"><para> 33 </para></entry><entry colsep="1" rowsep="1"><para> 38 </para></entry><entry colsep="1" rowsep="1"><para> 42 </para></entry><entry colsep="1" rowsep="1"><para> 45 </para></entry><entry colsep="1" rowsep="1"><para> 48 </para></entry><entry colsep="1" rowsep="1"><para> 51 </para></entry><entry colsep="1" rowsep="1"><para>  27 </para></entry><entry colsep="1" rowsep="1"><para> 30 </para></entry><entry colsep="1" rowsep="1"><para> 34 </para></entry><entry colsep="1" rowsep="1"><para> 37 </para></entry><entry colsep="1" rowsep="1"><para> 39 </para></entry><entry colsep="1" rowsep="1"><para> 42 </para></entry></row><row rowsep="1"><entry colsep="1" nameend="col_12" namest="col_0" rowsep="1"><para> 0.35 </para></entry><entry colsep="1" rowsep="1"><para> 28 </para></entry><entry colsep="1" rowsep="1"><para> 31 </para></entry><entry colsep="1" rowsep="1"><para> 34 </para></entry><entry colsep="1" rowsep="1"><para> 37 </para></entry><entry colsep="1" rowsep="1"><para> 40 </para></entry><entry colsep="1" rowsep="1"><para> 42 </para></entry><entry colsep="1" rowsep="1"><para>  22 </para></entry><entry colsep="1" rowsep="1"><para> 25 </para></entry><entry colsep="1" rowsep="1"><para> 28 </para></entry><entry colsep="1" rowsep="1"><para> 31 </para></entry><entry colsep="1" rowsep="1"><para> 33 </para></entry><entry colsep="1" rowsep="1"><para> 35 </para></entry></row><row rowsep="1"><entry colsep="1" nameend="col_12" namest="col_0" rowsep="1"><para> 0.40 </para></entry><entry colsep="1" rowsep="1"><para> 23 </para></entry><entry colsep="1" rowsep="1"><para> 27 </para></entry><entry colsep="1" rowsep="1"><para> 29 </para></entry><entry colsep="1" rowsep="1"><para> 32 </para></entry><entry colsep="1" rowsep="1"><para> 34 </para></entry><entry colsep="1" rowsep="1"><para> 36 </para></entry><entry colsep="1" rowsep="1"><para> 19 </para></entry><entry colsep="1" rowsep="1"><para> 22 </para></entry><entry colsep="1" rowsep="1"><para> 24 </para></entry><entry colsep="1" rowsep="1"><para> 26 </para></entry><entry colsep="1" rowsep="1"><para> 28 </para></entry><entry colsep="1" rowsep="1"><para> 30 </para></entry></row><row rowsep="1"><entry colsep="1" nameend="col_12" namest="col_0" rowsep="1"><para> 0.45 </para></entry><entry colsep="1" rowsep="1"><para> 20 </para></entry><entry colsep="1" rowsep="1"><para> 23 </para></entry><entry colsep="1" rowsep="1"><para> 25 </para></entry><entry colsep="1" rowsep="1"><para> 27 </para></entry><entry colsep="1" rowsep="1"><para> 29 </para></entry><entry colsep="1" rowsep="1"><para> 31 </para></entry><entry colsep="1" rowsep="1"><para>  16 </para></entry><entry colsep="1" rowsep="1"><para> 19 </para></entry><entry colsep="1" rowsep="1"><para> 21 </para></entry><entry colsep="1" rowsep="1"><para> 23 </para></entry><entry colsep="1" rowsep="1"><para> 25 </para></entry><entry colsep="1" rowsep="1"><para> 27 </para></entry></row><row rowsep="1"><entry colsep="1" nameend="col_12" namest="col_0" rowsep="1"><para> 0.50 </para></entry><entry colsep="1" rowsep="1"><para> 17 </para></entry><entry colsep="1" rowsep="1"><para> 20 </para></entry><entry colsep="1" rowsep="1"><para> 22 </para></entry><entry colsep="1" rowsep="1"><para> 24 </para></entry><entry colsep="1" rowsep="1"><para> 26 </para></entry><entry colsep="1" rowsep="1"><para>  27 </para></entry><entry colsep="1" rowsep="1"><para> 14 </para></entry><entry colsep="1" rowsep="1"><para> 16 </para></entry><entry colsep="1" rowsep="1"><para> 18 </para></entry><entry colsep="1" rowsep="1"><para> 20 </para></entry><entry colsep="1" rowsep="1"><para> 22 </para></entry><entry colsep="1" rowsep="1"><para> 23 </para></entry></row><row rowsep="1"><entry colsep="1" nameend="col_12" namest="col_0" rowsep="1"><para> 0.55 </para></entry><entry colsep="1" rowsep="1"><para> 15 </para></entry><entry colsep="1" rowsep="1"><para> 17 </para></entry><entry colsep="1" rowsep="1"><para> 19 </para></entry><entry colsep="1" rowsep="1"><para> 21 </para></entry><entry colsep="1" rowsep="1"><para> 23 </para></entry><entry colsep="1" rowsep="1"><para> 24 </para></entry><entry colsep="1" rowsep="1"><para>  12 </para></entry><entry colsep="1" rowsep="1"><para> 15 </para></entry><entry colsep="1" rowsep="1"><para> 16 </para></entry><entry colsep="1" rowsep="1"><para> 18 </para></entry><entry colsep="1" rowsep="1"><para> 20 </para></entry><entry colsep="1" rowsep="1"><para> 21 </para></entry></row><row rowsep="1"><entry colsep="1" nameend="col_12" namest="col_0" rowsep="1"><para> 0.60 </para></entry><entry colsep="1" rowsep="1"><para> 13 </para></entry><entry colsep="1" rowsep="1"><para> 15 </para></entry><entry colsep="1" rowsep="1"><para> 17 </para></entry><entry colsep="1" rowsep="1"><para> 19 </para></entry><entry colsep="1" rowsep="1"><para> 20 </para></entry><entry colsep="1" rowsep="1"><para> 22 </para></entry><entry colsep="1" rowsep="1"><para>  11 </para></entry><entry colsep="1" rowsep="1"><para> 13 </para></entry><entry colsep="1" rowsep="1"><para> 15 </para></entry><entry colsep="1" rowsep="1"><para> 16 </para></entry><entry colsep="1" rowsep="1"><para> 18 </para></entry><entry colsep="1" rowsep="1"><para> 19 </para></entry></row></tbody></tgroup></informaltable></section></article>