R help - May 2005 - 2 factor ANOVA and sphericity

With respect to calculating the epsilon index of sphericity for ANOVA, 
discussed on pp. 45-47 of:

http://www.psych.upenn.edu/~baron/rpsych.pdf

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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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 
- NOTE NEW EMAIL ADDRESS:
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:

http://www.psych.upenn.edu/~baron/rpsych.pdf

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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