<?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/pPowN</title><revhistory><revision><revnumber>14</revnumber><date>2013-03-08 10:17:12</date><authorinitials>localhost</authorinitials><revremark>converted to 1.6 markup</revremark></revision><revision><revnumber>13</revnumber><date>2007-07-13 11:11:11</date><authorinitials>PeterWatson</authorinitials></revision><revision><revnumber>12</revnumber><date>2007-07-13 11:11:03</date><authorinitials>PeterWatson</authorinitials></revision><revision><revnumber>11</revnumber><date>2007-07-13 11:09:54</date><authorinitials>PeterWatson</authorinitials></revision><revision><revnumber>10</revnumber><date>2007-01-15 09:52:51</date><authorinitials>PeterWatson</authorinitials></revision><revision><revnumber>9</revnumber><date>2007-01-15 09:52:26</date><authorinitials>PeterWatson</authorinitials></revision><revision><revnumber>8</revnumber><date>2007-01-09 16:07:25</date><authorinitials>PeterWatson</authorinitials></revision><revision><revnumber>7</revnumber><date>2007-01-09 16:07:06</date><authorinitials>PeterWatson</authorinitials></revision><revision><revnumber>6</revnumber><date>2007-01-09 16:03:05</date><authorinitials>PeterWatson</authorinitials></revision><revision><revnumber>5</revnumber><date>2006-10-23 11:24:37</date><authorinitials>PeterWatson</authorinitials></revision><revision><revnumber>4</revnumber><date>2006-10-23 11:15:30</date><authorinitials>PeterWatson</authorinitials></revision><revision><revnumber>3</revnumber><date>2006-10-23 11:10:32</date><authorinitials>PeterWatson</authorinitials></revision><revision><revnumber>2</revnumber><date>2006-10-18 14:02:33</date><authorinitials>PeterWatson</authorinitials></revision><revision><revnumber>1</revnumber><date>2006-10-18 13:59:38</date><authorinitials>PeterWatson</authorinitials></revision></revhistory></articleinfo><para>An on-line power calculator <ulink url="http://stat.ubc.ca/~rollin/stats/ssize/b1.html">is available.</ulink> </para><para>Computes total sample size needed for testing prop=const where prop and const are observed and expected (constant) proportions respectively and alpha is the (two-tailed) type I error for a given power. A calculator is available in a <ulink url="https://imaging.mrc-cbu.cam.ac.uk/statswiki/FAQ/power/pPowN/statswiki/FAQ/power/pPowN?action=AttachFile&amp;do=get&amp;target=propn.xls">spreadsheet.</ulink> </para><para>[COPY AND PASTE THE SYNTAX BELOW INTO A SPSS SYNTAX WINDOW AND RUN; SET DATA AS DESIRED]  </para><screen><![CDATA[DATA LIST free
/prop const alpha power. 
BEGIN DATA. 
0.45 0.5 .05 .85 
0.55 0.5 .05 .85
END DATA. 
]]><![CDATA[
set errors=none.
define propn (!pos !tokens(1)
                   / !pos !tokens(1)
                   / !pos !tokens(1)
                   / !pos !tokens(1)).
COMPUTE #POW = !4.
compute #conf = 1-!3.
compute #lc3 = 1.
compute #ind=0.
compute #chisq = 3.
comment COMPUTE #LC1 = 2.000.
COMPUTE #chisq1 = ((!1-!2)**2)/(!2*(1-!2)).
COMPUTE #CUMF2 =  1 - NCDF.CHISQ(IDF.CHISQ(#conf,1),1,#CHISQ).
compute #diff=1.
SET MXLOOPS=40000.
LOOP IF (#DIFF GT .00005) .
+       DO IF (#CUMF2 LT #pow) .
+               COMPUTE #LC3 = #CHISQ.
+               COMPUTE #CHISQ = (#chisq + 0.001).
+               COMPUTE #CUMF2 =  1 - NCDF.CHISQ(IDF.CHISQ(#conf,1),1,#CHISQ).
+       ELSE .
+               COMPUTE #LC1 = #chisq .
+               COMPUTE #chisq = (#chisq + #LC3)/2 .
+               COMPUTE #CUMF2 =  1 - NCDF.CHISQ(IDF.CHISQ(#conf,1),1,#CHISQ).
+       END IF .
+       COMPUTE #DIFF = ABS(#CUMF2 - #pow) .
END LOOP .
compute ntot = #chisq/#chisq1.
if (ntot-trunc(ntot) gt 0.5) #ind=1.
if (#ind eq 0) ntot=trunc(ntot)+1.
if (#ind eq 1) ntot=rnd(ntot).
EXECUTE .
compute prop=!1.
compute const=!2.
compute alpha=!3.
compute power=!4.
formats ntot (f7.0) alpha (f5.2) prop (f5.2) const (f5.2) power (f5.2).
variable labels ntot 'Sample Size Required' /alpha 'Alpha' /prop 'Observed Proportion' /const 'Constant' /power 'Power'.
report format=list automatic align(center)
  /variables=ntot alpha prop const power 
  /title "Sample Size required for a one sample binomial test" .
!enddefine.
]]><![CDATA[
matrix.
get m /variables=prop const alpha power  /missing=omit.
compute prop=make(1,1,0).
compute const=make(1,1,0).
compute alpha=make(1,1,0).
compute power=make(1,1,0).
compute prop=m(:,1).
compute const=m(:,2).
compute alpha=m(:,3).
compute power=m(:,4).  
end matrix.
propn prop const alpha power.]]></screen></article>