# Re: [R] 2 factor ANOVA and sphericity

From: John Sorkin <jsorkin_at_grecc.umaryland.edu>
Date: Thu 12 May 2005 - 14:50:43 EST

Darren is of course correct, but I hope the following, brief, intentionally non-technical explanation will help: Repeated measures analyses are needed only when there are three or more measurements from a given experimental unit and the two or more measurements are both on the right hand side of the equals sign, i.e. are independent variables. When there are only two observations, any one of the following models can be used, none of which have two measurements from the same experimental unit as independent variables.:

change (i.e. post-pre)=pre
post=pre

You will note that in both models only one observation from a given subject is on the right hand side of the equals sign, i.e. pre. When you have three observations from a given subject you generally need to have two or more observations on the right and side of the equals sign (unless you are doing something like a Markov Chain, but Markov Chains are beyond the scope of this Email.) and so need to consider repeated measures techniques.
John

John Sorkin M.D., Ph.D.
Chief, Biostatistics and Informatics
Baltimore VA Medical Center GRECC and
University of Maryland School of Medicine Claude Pepper OAIC

University of Maryland School of Medicine Division of Gerontology
Baltimore VA Medical Center
10 North Greene Street
GRECC (BT/18/GR)
Baltimore, MD 21201-1524

410-605-7119
jsorkin@grecc.umaryland.edu

>>> Darren Weber <darrenleeweber@gmail.com> 5/11/2005 6:40:09 PM >>>

With respect to calculating the epsilon index of sphericity for ANOVA,

discussed on pp. 45-47 of:

It notes that epsilon is not required for a repeated measures design with
only k=2 levels, as the minimum value of epsilon (e) is given by:

e = 1/(k-1)

so for k=2, we have e = 1 (ie, no correction of the F test df; see p. 46).
These notes apply to a univariate F test.

How do we estimate the minimum value of epsilon for a 2 factor ANOVA?

I have an experiment where we measure brain activity from the left and right
hemisphere, for two experimental conditions, in each subject. I consider the
measures from each hemisphere a repeated measures factor (2 levels) and the
experimental conditions is also a repeated measure (2 levels). The question
now is, how do we calculate epsilon for this 2 factor study and is it possible that epsilon could be anything < 1 when each factor has only 2

levels?

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