[R] nested, unbalanced anova

John Fox jfox at mcmaster.ca
Sun Jan 6 20:50:10 CET 2013

Dear Peter,

Thank you for the clarification, since one (I hope) popular add-on that
computes type-II and -III tests for repeated-measures designs is the Anova()
function in the car package. 

The type-II tests are, in my opinion, preferable, because they are maximally
powerful, e.g., for main effects when the interactions to which the main
effects are marginal are zero in the population (the situation in which a
main effect test is typically of interest), but I'd argue (not here, because
it would take more space than is reasonable in an email), that the type-III
tests test reasonably interpretable hypotheses.

Steven: A forthcoming paper in the R Journal, available as a preprint at
explains how to use the Anova() and linearHypothesis() functions in the car
package for univariate and multivariate tests in repeated-measures designs.
The paper doesn't, however, try to clarify the distinctions among "type-I,"
"II," and "III" tests.


John Fox
Senator McMaster Professor of Social Statistics
Department of Sociology
McMaster University
Hamilton, Ontario, Canada

> -----Original Message-----
> From: r-help-bounces at r-project.org [mailto:r-help-bounces at r-project.org]
> On Behalf Of peter dalgaard
> Sent: Sunday, January 06, 2013 1:56 PM
> To: peter dalgaard
> Cc: r-help at r-project.org
> Subject: Re: [R] nested, unbalanced anova
> On Jan 6, 2013, at 09:45 , peter dalgaard wrote:
> >
> > Just avoid things like Type-III sums of squares (base R won't do them,
> but popular add-ons will) because they get it wrong when cell counts are
> unequal.
> That might be a bit unfair. Type-III methodology has its proponents, I'm
> just not one of them. Within their own logic, I'm sure Type-III SS are
> computed correctly. It's just that this is one of the cases where you
> can be misled into thinking that the design is orthogonal so Type-III
> and Type-II is the same. It isn't.
> --
> Peter Dalgaard, Professor,
> Center for Statistics, Copenhagen Business School
> Solbjerg Plads 3, 2000 Frederiksberg, Denmark
> Phone: (+45)38153501
> Email: pd.mes at cbs.dk  Priv: PDalgd at gmail.com
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