R: st: repeated measures ANOVA to MANOVA - revisit

[<carlo.lazzaro@tiscalinet.it>]

Due to the low breakdown point of MANOVA about multivarite normality,
Ricardo may want to run a repeated MANOVA on observations and then ranks,
compare the results and check if the latter approach confirms the finding of
the first one.
Kindest Regards,
Carlo
-----Messaggio originale-----
Da: owner-statalist@hsphsun2.harvard.edu
[mailto:owner-statalist@hsphsun2.harvard.edu] Per conto di Lachenbruch,
Peter
Inviato: sabato 4 febbraio 2012 02:28
A: statalist@hsphsun2.harvard.edu
Oggetto: RE: st: repeated measures ANOVA to MANOVA - revisit

There is also the issue of robustness to multivariate normality.  MANOVA has
a low breakdown point.  If using MANOVA, consider doing a permutation test
approach.

________________________________________
From: owner-statalist@hsphsun2.harvard.edu
[owner-statalist@hsphsun2.harvard.edu] On Behalf Of khigbee@stata.com
[khigbee@stata.com]
Sent: Friday, February 03, 2012 1:42 PM
To: statalist@hsphsun2.harvard.edu
Subject: Re: st: repeated measures ANOVA to MANOVA - revisit

Ricardo Ovaldia <ovaldia@yahoo.com> is concerned because the p-value from
the repeated measures ANOVA

> . reshape long m, i(id) j(method)
> . anova m id  method, repeat( method)

produces Huynh-Feldt corrected p-value of about .0020 while the MANOVA

> . gen myconst=1
> . manova m1 m2 m3= myconst, nocons
> . mat c = (1,0,-1\0,1,-1)
> . manovatest mycons, ytransform(c)

produces a p-value of about .00000025.

When MANOVA can be run (i.e., you have enough observations so that the
needed matrices do not become singular (or near singular)), I prefer to use
it.  ANOVA for repeated measures has to rely on correction factors to try to
overcome the violation of independence of observations (which will usually
be violated with repeated measures data) while MANOVA does not need a
correction factor.

The ANOVA and MANOVA approaches are not equivalent, hence different results
in your p-values.

I think you will find useful advice in Rencher (2002) starting at page 204
where he compares the two approaches.

Rencher, A.C. 2002.  Mthods of Multivariate Analysis. 2nd ed.
    New York: Wiley.

Ken Higbee
khigbee@stata.com

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