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RE: st: repeated measures ANOVA to MANOVA - revisit


From   "Lachenbruch, Peter" <Peter.Lachenbruch@oregonstate.edu>
To   "statalist@hsphsun2.harvard.edu" <statalist@hsphsun2.harvard.edu>
Subject   RE: st: repeated measures ANOVA to MANOVA - revisit
Date   Fri, 3 Feb 2012 17:27:59 -0800

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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