[R] ANOVA non-sphericity test and corrections (eg, Greenhouse-Geisser)

[Peter Dalgaard]

DarrenWeber wrote:
> I'm an experimental psychologist and when I run ANOVA analysis in
> SPSS, I normally ask for a test of non-sphericity (Box's M-test).  I
> also ask for output of the corrections for non-sphericity, such as
> Greenhouse-Geisser and Huhn-Feldt.  These tests and correction factors
> are commonly used in the journals for experimental and other
> psychology reports.  I have been switching from SPSS to R for over a
> year now, but I realize now that I don't have the non-sphericity test
> and correction factors.
>   
This can be done using anova.mlm() and mauchly.test()  which work on 
"mlm" objects, i.e., lm() output where the response is a matrix. There 
is no theory, to my knowledge, to support it for general aov() models, 
the catch being that you need to have a within-subject covariance matrix.