repeated measures anova, sphericity, epsilon, etc

I have 3 questions (below).

Background: I am teaching an introductory statistics course in which we are
covering (among other things) repeated measures anova. This time around
teaching it, we are using R for all of our computations. We are starting by
covering the univariate approach to repeated measures anova.

Doing a basic repeated measures anova (univariate approach) using aov()
seems straightforward (e.g.:

+> myModel<-aov(myDV~myFactor+Error(Subjects/myFactor),data=myData)
+> summary(myModel)

Where I am currently stuck is how best to deal with the issue of the
assumption of homogeneity of treatment differences (in other words, the
sphericity assumption) - both how to test it in R and how to compute
corrected df for the F-test if the assumption is violated.

Back when I taught this course using SPSS it was relatively straightforward
- we would look at Mauchly's test of sphericity - if it was significant,
then we would use one of the corrected F-tests (e.g. Greenhouse-Geisser or
Huynh-Feldt) that were spat out automagically by SPSS.

I gather from searching the r-help archives, searching google, and searching
through various books on R, that the only way of using mauchly.test() in R
is on a multivariate model object (e.g. mauchly.test cannot handle an aov()
object).

Question 1: how do you (if you do so), test for sphericity in a repeated
measures anova using R, when using aov()? (or do you test the sphericity
assumption using a different method)?

Question 2: Can someone point me to an example (on the web, in a book,
wherever) showing how to perform a repeated measures anova using the
multivariate approach in R?

Question 3: Are there any existing R functions for calculating adjusted df
for Greenhouse-Geisser, Huynh-Feldt (or calculating epsilon), or is it up to
me to write my own function?

Thanks in advance for any suggestions,

am2 <- lme(dv ~ myfactor, random = ~1|subject/myfactor, data=mydata)
intervals(am2)

After much research I've listed a couple of ways to do repeated measures
anova here:

http://gribblelab.org/2009/03/09/repeated-measures-anova-using-r/

including univariate and multivariate methods, post-hoc tests, sphericity
test, etc.

It appears to me that the most useful way is a multivariate model and then
using Anova() from the car package.

-Paul


On Tue, Mar 3, 2009 at 5:37 PM, Paul Gribble <pgribble at uwo.ca> wrote:

Have a look at

http://cran.r-project.org/doc/Rnews/Rnews_2007-2.pdf

Wow. I think my students would keel over.


Anova() from the car package looks promising - I will check it out. Thanks



On Tue, Mar 3, 2009 at 4:00 PM, Peter Dalgaard <p.dalgaard at biostat.ku.dk>wrote:

Paul Gribble wrote:

I have 3 questions (below).

Background: I am teaching an introductory statistics course in which we
are
covering (among other things) repeated measures anova. This time around
teaching it, we are using R for all of our computations. We are starting
by
covering the univariate approach to repeated measures anova.

Doing a basic repeated measures anova (univariate approach) using aov()
seems straightforward (e.g.:

+> myModel<-aov(myDV~myFactor+Error(Subjects/myFactor),data=myData)
+> summary(myModel)

Where I am currently stuck is how best to deal with the issue of the
assumption of homogeneity of treatment differences (in other words, the
sphericity assumption) - both how to test it in R and how to compute
corrected df for the F-test if the assumption is violated.

Back when I taught this course using SPSS it was relatively
straightforward
- we would look at Mauchly's test of sphericity - if it was significant,
then we would use one of the corrected F-tests (e.g. Greenhouse-Geisser
or
Huynh-Feldt) that were spat out automagically by SPSS.

I gather from searching the r-help archives, searching google, and
searching
through various books on R, that the only way of using mauchly.test() in
R
is on a multivariate model object (e.g. mauchly.test cannot handle an
aov()
object).

Question 1: how do you (if you do so), test for sphericity in a repeated
measures anova using R, when using aov()? (or do you test the sphericity
assumption using a different method)?

Question 2: Can someone point me to an example (on the web, in a book,
wherever) showing how to perform a repeated measures anova using the
multivariate approach in R?

Question 3: Are there any existing R functions for calculating adjusted
df
for Greenhouse-Geisser, Huynh-Feldt (or calculating epsilon), or is it up
to
me to write my own function?

Thanks in advance for any suggestions,

Have a look at

http://cran.r-project.org/doc/Rnews/Rnews_2007-2.pdf

Last time this came up, John Fox also pointed to some of his stuff, see
http://finzi.psych.upenn.edu/R/Rhelp08/archive/151282.html

--
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--
Paul L. Gribble, Ph.D.
Associate Professor
Dept. Psychology
The University of Western Ontario
London, Ontario
Canada N6A 5C2
Tel. +1 519 661 2111 x82237
Fax. +1 519 661 3961
pgribble at uwo.ca
http://gribblelab.org

--
Paul L. Gribble, Ph.D.
Associate Professor
Dept. Psychology
The University of Western Ontario
London, Ontario
Canada N6A 5C2
Tel. +1 519 661 2111 x82237
Fax. +1 519 661 3961
pgribble at uwo.ca
http://gribblelab.org

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