[R] Type-I v/s Type-III Sum-Of-Squares in ANOVA

Frank E Harrell Jr f.harrell at Vanderbilt.Edu
Mon Mar 1 16:23:15 CET 2010

I continue to be surprised that the majority of users do not search the 
help archives linked from www.r-project.org.  This is a much discussed 
topic, including vast amounts of information on the silliness of type 
III tests.


Ravi Kulkarni wrote:
> Hello,
>   I believe the aov() function in R uses a "Type-I sum-of-squares" by
> default as against "Type-III".
>   This is relevant for me because I am trying to understand ANOVA in R using
> my knowledge of ANOVA in SPSS. I can only reproduce the results of an ANOVA
> done using R through SPSS if I specify that SPSS uses a Type-I
> sum-of-squares. (And yes, I know that when the sample sizes of all groups
> are equal, Type-I and Type-III produce the same answers.)
>   My questions: 1) exactly what is the difference between the two types of
> sums-of-squares?
>                       2) how can I make R use a Type-III s-o-s? Should I? R
> must have some reason for using Type-I as default rather than Type-III.
> (Given a choice, believe R!)
> A reference (stats book, URL...) would be helpful...
> Ravi

Frank E Harrell Jr   Professor and Chairman        School of Medicine
                      Department of Biostatistics   Vanderbilt University

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