<?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/ResidualsNonNormality</title><revhistory><revision><revnumber>6</revnumber><date>2013-03-08 10:17:44</date><authorinitials>localhost</authorinitials><revremark>converted to 1.6 markup</revremark></revision><revision><revnumber>5</revnumber><date>2010-09-21 13:48:57</date><authorinitials>PeterWatson</authorinitials></revision><revision><revnumber>4</revnumber><date>2010-09-21 13:46:10</date><authorinitials>PeterWatson</authorinitials></revision><revision><revnumber>3</revnumber><date>2006-06-30 22:57:01</date><authorinitials>Scripting Subsystem</authorinitials></revision><revision><revnumber>2</revnumber><date>2006-06-30 22:55:29</date><authorinitials>Scripting Subsystem</authorinitials></revision><revision><revnumber>1</revnumber><date>2006-06-30 21:37:50</date><authorinitials>Scripting Subsystem</authorinitials></revision></revhistory></articleinfo><section><title>Residuals and Non-normality</title><para>This page will give some tips on aspects of looking at residuals in order to assess non-normality. In particular it will stress how </para><itemizedlist><listitem><para>in repeated measures data, the thing that matters is the distributions of differences between pairs of measures (or more general contrasts in the repeated measures). </para></listitem><listitem><para>in grouped data, it is the residuals adjusted for group means that matter </para></listitem></itemizedlist><para>Consider this very small example: </para><informaltable><tgroup cols="2"><colspec colname="col_0" colwidth="50*"/><colspec colname="col_1" colwidth="50*"/><tbody><row rowsep="1"><entry colsep="1" rowsep="1"><para> <emphasis role="strong">X1</emphasis> </para></entry><entry colsep="1" rowsep="1"><para><emphasis role="strong">X2</emphasis></para></entry></row><row rowsep="1"><entry colsep="1" rowsep="1"><para> 1 </para></entry><entry colsep="1" rowsep="1"><para>  2 </para></entry></row><row rowsep="1"><entry colsep="1" rowsep="1"><para> 2 </para></entry><entry colsep="1" rowsep="1"><para> 1  </para></entry></row><row rowsep="1"><entry colsep="1" rowsep="1"><para> 3 </para></entry><entry colsep="1" rowsep="1"><para> 2 </para></entry></row><row rowsep="1"><entry colsep="1" rowsep="1"><para> 1001 </para></entry><entry colsep="1" rowsep="1"><para> 1002 </para></entry></row></tbody></tgroup></informaltable><para>The distributions of the variables are very skewed.  The distribution of the differences (for a repeated measures t-test) are at least symmetrical, if not normal. [Last updated on 21 September, 2010] </para><!--rule (<hr>) is not applicable to DocBook--><para> <ulink url="https://imaging.mrc-cbu.cam.ac.uk/statswiki/FAQ/ResidualsNonNormality/statswiki/FAQ#">Return to Statistics FAQ page</ulink> </para><para><ulink url="https://imaging.mrc-cbu.cam.ac.uk/statswiki/FAQ/ResidualsNonNormality/statswiki/CbuStatistics#">Return to Statistics main page</ulink> </para><para><ulink url="http://www.mrc-cbu.cam.ac.uk/">Return to CBU main page</ulink> </para><para>These pages are maintained by <ulink url="mailto:ian.nimmo-smith@mrc-cbu.cam.ac.uk">Ian Nimmo-Smith</ulink> and <ulink url="mailto:peter.watson@mrc-cbu.cam.ac.uk">Peter Watson</ulink> </para></section></article>