# [R] 2 factor ANOVA and sphericity

From: Darren Weber <darrenleeweber_at_gmail.com>
Date: Thu 12 May 2005 - 08:40:09 EST

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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