<?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/powprogs</title><revhistory><revision><revnumber>29</revnumber><date>2017-08-25 12:19:05</date><authorinitials>PeterWatson</authorinitials></revision><revision><revnumber>28</revnumber><date>2017-08-25 12:18:24</date><authorinitials>PeterWatson</authorinitials></revision><revision><revnumber>27</revnumber><date>2017-08-25 12:18:10</date><authorinitials>PeterWatson</authorinitials></revision><revision><revnumber>26</revnumber><date>2017-08-25 12:17:50</date><authorinitials>PeterWatson</authorinitials></revision><revision><revnumber>25</revnumber><date>2017-06-02 12:14:00</date><authorinitials>PeterWatson</authorinitials></revision><revision><revnumber>24</revnumber><date>2017-06-02 12:12:44</date><authorinitials>PeterWatson</authorinitials></revision><revision><revnumber>23</revnumber><date>2017-06-02 12:11:53</date><authorinitials>PeterWatson</authorinitials></revision><revision><revnumber>22</revnumber><date>2017-06-02 12:11:27</date><authorinitials>PeterWatson</authorinitials></revision><revision><revnumber>21</revnumber><date>2017-06-02 12:11:13</date><authorinitials>PeterWatson</authorinitials></revision><revision><revnumber>20</revnumber><date>2017-06-02 12:10:26</date><authorinitials>PeterWatson</authorinitials></revision><revision><revnumber>19</revnumber><date>2017-03-28 15:00:04</date><authorinitials>PeterWatson</authorinitials></revision><revision><revnumber>18</revnumber><date>2017-03-28 14:59:45</date><authorinitials>PeterWatson</authorinitials></revision><revision><revnumber>17</revnumber><date>2017-03-28 14:59:28</date><authorinitials>PeterWatson</authorinitials></revision><revision><revnumber>16</revnumber><date>2017-03-28 14:51:42</date><authorinitials>PeterWatson</authorinitials></revision><revision><revnumber>15</revnumber><date>2017-03-28 14:45:12</date><authorinitials>PeterWatson</authorinitials></revision><revision><revnumber>14</revnumber><date>2017-03-28 14:42:50</date><authorinitials>PeterWatson</authorinitials></revision><revision><revnumber>13</revnumber><date>2017-03-27 09:21:02</date><authorinitials>PeterWatson</authorinitials></revision><revision><revnumber>12</revnumber><date>2017-03-27 09:20:00</date><authorinitials>PeterWatson</authorinitials></revision><revision><revnumber>11</revnumber><date>2016-12-02 10:30:25</date><authorinitials>PeterWatson</authorinitials></revision><revision><revnumber>10</revnumber><date>2016-12-02 10:29:15</date><authorinitials>PeterWatson</authorinitials></revision><revision><revnumber>9</revnumber><date>2015-10-05 08:50:52</date><authorinitials>PeterWatson</authorinitials></revision><revision><revnumber>8</revnumber><date>2015-02-09 13:58:53</date><authorinitials>PeterWatson</authorinitials></revision><revision><revnumber>7</revnumber><date>2014-01-15 10:11:22</date><authorinitials>PeterWatson</authorinitials></revision><revision><revnumber>6</revnumber><date>2014-01-15 10:10:13</date><authorinitials>PeterWatson</authorinitials></revision><revision><revnumber>5</revnumber><date>2014-01-15 10:09:48</date><authorinitials>PeterWatson</authorinitials></revision><revision><revnumber>4</revnumber><date>2014-01-15 10:07:06</date><authorinitials>PeterWatson</authorinitials></revision><revision><revnumber>3</revnumber><date>2013-08-07 13:08:46</date><authorinitials>PeterWatson</authorinitials></revision><revision><revnumber>2</revnumber><date>2013-03-08 10:17:14</date><authorinitials>localhost</authorinitials><revremark>converted to 1.6 markup</revremark></revision><revision><revnumber>1</revnumber><date>2012-06-26 14:38:36</date><authorinitials>PeterWatson</authorinitials></revision></revhistory></articleinfo><section><title>Power computations</title><para>Power computations can be performed in SPSS and R using syntax. For SPSS users Chris Aberson has syntax for power calculations in his book. See reference below. </para><para><emphasis role="underline">Note</emphasis> in SPSS Version 24 and later one can add in R extensions to perform power analyses via the Extensions&gt;Extension hub which adds the R programs to the SPSS gui menu so power computations can be performed in SPSS with 'point and click'. Alternatively one could use these procedures in R with syntax. </para><para>For a theoretical background and details of specialist software have a look at graduate seminar on power at the <ulink url="https://lsr-wiki-01.mrc-cbu.cam.ac.uk/statswiki/FAQ/powprogs/statswiki/StatsCourse2006#">Graduate Statistics Programme October-December 2006</ulink>. There is also <ulink url="http://homepages.gold.ac.uk/aphome/cc16work.doc">a worked example</ulink> using &quot;Method 2&quot; on a t-test. <ulink url="https://lsr-wiki-01.mrc-cbu.cam.ac.uk/statswiki/FAQ/powprogs/statswiki/FAQ/powprogs?action=AttachFile&amp;do=get&amp;target=vif.pdf">F. Y. Hsieh, Philip W. Lavori, Harvey J. Cohen and John R. Feussner (2003) An Overview of Variance Inflation Factors for Sample-Size Calculation</ulink> <emphasis>Eval Health Prof</emphasis> <emphasis role="strong">26</emphasis> 239-257 mentions various formulae for power calculations. </para><para>Note in some cases one needs to inflate the total sample size required if there is a natural clustering in the data such as patients being assessed by different exercise therapists. For example if there are b patients assessed by each exercise therapist with an intra-therapist correlation (ICC) then the design effect equals 1 + [(b-1)ICC]. The total sample needs to be multiplied by this design effect to give sample size adjusted for the clustering effect. A further adjustment for variations in cluster sizes can be made (measured by the coefficient of variation) can be incorporated into the formula giving DE =  1 + (b(1+cv^2)-1)ICC. This extra adjustment for differing cluster sizes is not needed for small cvs e.g. cv &lt; 0.23 (see <ulink url="https://lsr-wiki-01.mrc-cbu.cam.ac.uk/statswiki/FAQ/powprogs/statswiki/FAQ/powprogs?action=AttachFile&amp;do=get&amp;target=cvDE.pdf">page 26 of this presentation</ulink>). </para><para><emphasis role="underline">Sample sizes required for a given power</emphasis> </para><itemizedlist><listitem><para><ulink url="https://lsr-wiki-01.mrc-cbu.cam.ac.uk/statswiki/FAQ/powprogs/statswiki/FAQ/power/onesamp#">One sample t-test</ulink> </para></listitem><listitem><para><ulink url="https://lsr-wiki-01.mrc-cbu.cam.ac.uk/statswiki/FAQ/powprogs/statswiki/FAQ/power/unpaired#">Unpaired t-tests (equal group sizes)</ulink> </para></listitem><listitem><para><ulink url="https://lsr-wiki-01.mrc-cbu.cam.ac.uk/statswiki/FAQ/powprogs/statswiki/FAQ/power/unpairedUneq#">Unpaired t-tests (unequal group sizes)</ulink> </para></listitem><listitem><para><ulink url="https://lsr-wiki-01.mrc-cbu.cam.ac.uk/statswiki/FAQ/powprogs/statswiki/FAQ/power/pairt#">Paired t-tests</ulink> </para></listitem><listitem><para><ulink url="https://lsr-wiki-01.mrc-cbu.cam.ac.uk/statswiki/FAQ/powprogs/statswiki/FAQ/power/owAnovaN#">Regression including One-Way ANOVA and ANCOVA</ulink> </para></listitem><listitem><para><ulink url="https://lsr-wiki-01.mrc-cbu.cam.ac.uk/statswiki/FAQ/powprogs/statswiki/FAQ/power/pPowN#">Comparing a single proportion with a constant (sign test)</ulink> </para></listitem><listitem><para><ulink url="https://lsr-wiki-01.mrc-cbu.cam.ac.uk/statswiki/FAQ/powprogs/statswiki/FAQ/power/propsn#">Comparing two independent proportions</ulink> </para></listitem><listitem><para><ulink url="https://lsr-wiki-01.mrc-cbu.cam.ac.uk/statswiki/FAQ/powprogs/statswiki/FAQ/power/prop1sn#">Comparing three or more independent proportions</ulink> </para></listitem><listitem><para><ulink url="https://lsr-wiki-01.mrc-cbu.cam.ac.uk/statswiki/FAQ/powprogs/statswiki/FAQ/power/mcn#">Comparing two related proportions (McNemar test)</ulink> </para></listitem><listitem><para><ulink url="https://lsr-wiki-01.mrc-cbu.cam.ac.uk/statswiki/FAQ/powprogs/statswiki/FAQ/power/FisherrN#">Comparing two independent correlations from two different samples</ulink> </para></listitem><listitem><para><ulink url="https://lsr-wiki-01.mrc-cbu.cam.ac.uk/statswiki/FAQ/powprogs/statswiki/FAQ/power/rmPowN#">A term in any Anova (including repeated measures)</ulink> </para></listitem><listitem><para><ulink url="https://lsr-wiki-01.mrc-cbu.cam.ac.uk/statswiki/FAQ/powprogs/statswiki/FAQ/power/llogN#">A single predictor in a multiple binary logistic regression</ulink> </para></listitem><listitem><para><ulink url="https://lsr-wiki-01.mrc-cbu.cam.ac.uk/statswiki/FAQ/powprogs/statswiki/FAQ/power/hazN#">Survival analysis</ulink> </para></listitem></itemizedlist><para><emphasis role="underline">Power required for given sample sizes</emphasis> </para><itemizedlist><listitem><para><ulink url="https://lsr-wiki-01.mrc-cbu.cam.ac.uk/statswiki/FAQ/powprogs/statswiki/FAQ/power/onesampn#">One sample t-test</ulink> </para></listitem><listitem><para><ulink url="https://lsr-wiki-01.mrc-cbu.cam.ac.uk/statswiki/FAQ/powprogs/statswiki/FAQ/power/unpaireqn#">Unpaired t-tests (equal group sizes)</ulink> </para></listitem><listitem><para><ulink url="https://lsr-wiki-01.mrc-cbu.cam.ac.uk/statswiki/FAQ/powprogs/statswiki/FAQ/power/unpairn#">Unpaired t-tests (unequal group sizes)</ulink> </para></listitem><listitem><para><ulink url="https://lsr-wiki-01.mrc-cbu.cam.ac.uk/statswiki/FAQ/powprogs/statswiki/FAQ/power/pairn#">Paired t-tests</ulink> </para></listitem><listitem><para><ulink url="https://lsr-wiki-01.mrc-cbu.cam.ac.uk/statswiki/FAQ/powprogs/statswiki/FAQ/power/owanova#">Regression including One-Way ANOVA and ANCOVA</ulink> </para></listitem><listitem><para><ulink url="https://lsr-wiki-01.mrc-cbu.cam.ac.uk/statswiki/FAQ/powprogs/statswiki/FAQ/power/pPow#">Comparing a single proportion with a constant (sign test)</ulink> </para></listitem><listitem><para><ulink url="https://lsr-wiki-01.mrc-cbu.cam.ac.uk/statswiki/FAQ/powprogs/statswiki/FAQ/power/props#">Comparing two independent proportions</ulink> </para></listitem><listitem><para><ulink url="https://lsr-wiki-01.mrc-cbu.cam.ac.uk/statswiki/FAQ/powprogs/statswiki/FAQ/power/prop1s#">Comparing three or more independent proportions</ulink> </para></listitem><listitem><para><ulink url="https://lsr-wiki-01.mrc-cbu.cam.ac.uk/statswiki/FAQ/powprogs/statswiki/FAQ/power/mcnemarN#">Comparing two related proportions (McNemar test)</ulink> </para></listitem><listitem><para><ulink url="https://lsr-wiki-01.mrc-cbu.cam.ac.uk/statswiki/FAQ/powprogs/statswiki/FAQ/power/Fisherr#">Comparing two independent correlations from two different samples</ulink> </para></listitem><listitem><para><ulink url="https://lsr-wiki-01.mrc-cbu.cam.ac.uk/statswiki/FAQ/powprogs/statswiki/FAQ/power/rmPow#">A term in any Anova (including repeated measures)</ulink> </para></listitem><listitem><para><ulink url="https://lsr-wiki-01.mrc-cbu.cam.ac.uk/statswiki/FAQ/powprogs/statswiki/FAQ/power/llogPow#">A single predictor in a multiple binary logistic regression</ulink> </para></listitem><listitem><para><ulink url="https://lsr-wiki-01.mrc-cbu.cam.ac.uk/statswiki/FAQ/powprogs/statswiki/FAQ/power/haz#">Survival analysis</ulink> </para></listitem><listitem><para><ulink url="https://lsr-wiki-01.mrc-cbu.cam.ac.uk/statswiki/FAQ/powprogs/statswiki/FAQ/power/roc#">ROC Analysis</ulink> </para></listitem></itemizedlist><para>Additional power freeware (including the popular G*POWER (currently version 3)) is available  for download from <ulink url="http://www.epibiostat.ucsf.edu/biostat/sampsize.html#PCSize">here.</ulink> Some examples using G*POWER 3 are in Howell (2013). There are also some power calculators mentioned in the Power Grad talks and <ulink url="http://powerandsamplesize.com/Calculators">here including Survival Analysis power computations here</ulink> and for Relative Risk <ulink url="https://www.stat.ubc.ca/~rollin/stats/ssize/caco.html">here</ulink> where the calculations are the same as in <emphasis role="underline">Comparing Proportions for Two Independent Samples</emphasis> setting p1=p0 (probability of adverse event in the control group) and p2= p0*RR/(1 + p0*(RR - 1)). See Schesselman, J. (1982), Case Control Studies, p. 145. Risk Ratios are ratios of group probabilities of a negative event where Odds Ratios are ratios of the group odds of a negative event <ulink url="http://www.theanalysisfactor.com/the-difference-between-relative-risk-and-odds-ratios/">as described here.</ulink> </para><para>Other power calculators  <ulink url="http://www.ai-therapy.com/psychology-statistics/effect-size-calculator">here.</ulink> </para><para><emphasis role="underline">References</emphasis> </para><para>Aberson CL (2010) Applied power analysis for the behavioral sciences. Routledge:London. This book contains examples of computing effect sizes and power using SPSS. </para><para>Howell DC (2013) Statistical methods for psychology. 8th Edition. International Edition. Wadsworth:Belmont,CA. </para></section></article>