<?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/MANOVA/manrm/sphericity</title><revhistory><revision><revnumber>2</revnumber><date>2013-03-08 10:17:18</date><authorinitials>localhost</authorinitials><revremark>converted to 1.6 markup</revremark></revision><revision><revnumber>1</revnumber><date>2007-02-22 16:16:59</date><authorinitials>PeterWatson</authorinitials></revision></revhistory></articleinfo><section><title>More on Sphericity</title><para>The general algorithm implemented will attempt to generate, for each effect,  a set of independent (orthogonal) contrasts. In repeated measures ANOVA, these  contrasts specify a set of  hypotheses about differences between the levels  of the repeated measures factor. However, if these differences are correlated  across subjects, then the resulting contrasts are no longer independent.  For example, in a study where we measured learning at three times during the  experimental session, it may happen that the changes from time 1 to time 2 are  negatively correlated with the changes from time 2 to time 3: subjects who  learn most of the material between time 1 and time 2 improve less from time 2  to time 3. In fact, in most instances where a repeated measures ANOVA is used,  one would probably suspect that the changes across levels are correlated  across subjects. However, when this happens, the compound symmetry and  sphericity assumptions have been violated, and independent contrasts cannot be  computed.  </para><para>(Taken from  <ulink url="http://www.statsoft.com/textbook/stanman.html"/>.) </para></section></article>