<?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/nonp/pooledes</title><revhistory><revision><revnumber>5</revnumber><date>2013-03-08 10:17:16</date><authorinitials>localhost</authorinitials><revremark>converted to 1.6 markup</revremark></revision><revision><revnumber>4</revnumber><date>2013-02-11 14:52:22</date><authorinitials>PeterWatson</authorinitials></revision><revision><revnumber>3</revnumber><date>2013-02-11 14:50:24</date><authorinitials>PeterWatson</authorinitials></revision><revision><revnumber>2</revnumber><date>2013-02-11 14:49:59</date><authorinitials>PeterWatson</authorinitials></revision><revision><revnumber>1</revnumber><date>2013-02-11 14:49:52</date><authorinitials>PeterWatson</authorinitials></revision></revhistory></articleinfo><section><title>Obtaining z as input to Rosenthal formula on previous page for a nonparametric analysis using three or more groups</title><para>If you really want to quote an effect size for the pooled analysis ie comparing all the groups at once then you could estimate z as below (again following Field, 2005): </para><orderedlist numeration="arabic"><listitem><para>Obtain the one or two-sided p-value for the chi-square for the data from using the Kruskal-Wallis and/or chi-square test (it will have more than one df) </para></listitem><listitem><para> Find the z value that has the same one or two-sided p-value as that obtained just now for the chi-square. You can do this using a function in any stats package or in Excel. </para></listitem></orderedlist><para>For example in SPSS: suppose the two-sided p-value of my chi-square from doing either a Kruskal-Wallis or chi-square test is 0.02. Running the below </para><screen><![CDATA[COMPUTE PIN=0.02.
COMPUTE P=1-(PIN/2).
COMPUTE ZOUT=IDF.NORMAL(P,0,1).
EXE.]]></screen><para>gives a z of 2.326 so for a total sample size of 40 the the effect size = 2.326/sqrt(40)= 0.367. Alternatively you could run this from the gui choosing the 'compute' option. </para><para>If you are using a one-tailed test and, for example, had a one-sided p=0.01 then we could instead tweak the above and use the below </para><screen><![CDATA[COMPUTE PIN=0.01.
COMPUTE P=1-(PIN).
COMPUTE ZOUT=IDF.NORMAL(P,0,1).
EXE.]]></screen><para>which gives a z=1.645. </para></section></article>