<- file stat 97comsym.html -> Here is a brief discussion of compound symmetry and sphericity assumptions (Cross) in repeated measures. *----------------

Compound symmetry

=======================David Cross, 25 Jan 1997==========sse Message-ID: <Pine.PMDF.3.91.970125180749.420374A-100000@GAMMA.IS.TCU.EDU> From: David Cross <cross@GAMMA.IS.TCU.EDU> Subject: RE: Compound Symmetry " In repeated measures designs, I've come across 2 assumptions: compound symmetry and sphericity. Are they different terms for the same assumption?" The best explanation I have seen of the assumptions surrounding the univariate approach to repeated measures is to be found in Maxwell & Delaney (1990) Designing experiments and analyzing data: A model comparison perspective. I will give you the gist of their discussion, but you will probably want to refer to their text (pp. 471-474). First, in addition to the usual assumptions of the between subjects design (i.e. normality, indepedence, homogeneity of variance), the within subjects design requires homogeneity of treatment difference variances. (One can create a new set of variables, composed of all possible pairwise differences, and the variances of these differences must all be equal in the population.) Second, it can be shown that this assumption is equivalent to the sphericity assumption. Third, the compound symmetry assumption is a special case of the sphericity assumption (i.e. if compound symmetry is satisfied, then sphericity is satisfied). Compound symmetry requires of the original repeated measures that (a) all the variances be equal in the population, and (b) all the covariances be equal in the population. Hope this helps, * * * * * * * * * * * * * * * * * * * * * * * * * * * * *

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