[R] Type III sum of squares and appropriate contrasts

Greg Snow Greg.Snow at intermountainmail.org
Thu Oct 11 19:45:23 CEST 2007

Using type III sums of squares with non-orthogonal contrasts is like the
classic grade school puzzle:

"3 men decide to share a hotel room that costs $30, so each pays $10.
The maneger realizes that the room they received is only $25 and sends
$5 back with the bellboy.  The bellboy realizes that there is no good
way to split $5 3 ways decides to help them all by giving each man $1
and keeping $2 for himself.  So each man has now paid $9 for a total of
$27, add the $2 that the bellboy kept and you get $29, but the original
total was $30.  Where is the missing $1?"

It may also be enlightening to load the fortunes package and type:
fortune("III") several times.

Gregory (Greg) L. Snow Ph.D.
Statistical Data Center
Intermountain Healthcare
greg.snow at intermountainmail.org
(801) 408-8111

> -----Original Message-----
> From: r-help-bounces at r-project.org 
> [mailto:r-help-bounces at r-project.org] On Behalf Of Menelaos 
> Stavrinides
> Sent: Thursday, October 11, 2007 11:24 AM
> To: r-help at r-project.org
> Subject: [R] Type III sum of squares and appropriate contrasts
> I am running a two-way anova with Type III sums of squares 
> and would like to be able to understand what the different SS 
> mean when I use different contrasts, e.g. treatment contrasts 
> vs helmert contrasts. I have read John Fox's "An R and S-Plus 
> Companion to Applied Regression"
> approach -p. 140- suggesting that treatment contrasts do not 
> usually result in meaningful results with Type III SS but 
> it's not clear to me why. Any suggestions on a stats text 
> discussing this would be greatly appreciated.
> Thanks,
> Mel
> --
> Menelaos Stavrinides
> Ph.D. Candidate
> Environmental Science, Policy and Management
> 137 Mulford Hall MC #3114
> University of California
> Berkeley, CA 94720-3114 USA
> Tel: 510 717 5249
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