Type I and Type III SS in anova

Dear list,

slightly OT: can you recommend me any sources where I can find more about 
this Type I - II - III anova problem? It seems as my statistics courses did 
not cover this issue, so I feel rather naive and have this sort of feeling 
that some of my analyses might be complete nonsense.

Regards,
Stefan

John Fox schrieb, Am 26.09.2008 12:36:

Dear Menelaos,

-----Original Message-----
From: r-help-bounces at r-project.org [mailto:r-help-bounces at r-project.org]

On

Behalf Of Menelaos Stavrinides
Sent: September-25-08 9:56 PM
To: r-help at r-project.org
Subject: [R] Type I and Type III SS in anova

Hi all,
I have been trying to calculate Type III SS in R for an unbalanced two-way
anova. However, the Type III SS are lower for the first factor compared to
type I but higher for the second factor (see below). I have the impression
that Type III are always lower than Type I - is that right?

No.

And a clarification about how to fit Type III SS. Fitting

model<-aov(y~a*b)

in the base package and then loading car / changing contrasts / running
Anova(model,type=c("III")) gives different results compared to loading car

/

changing contrasts / fitting model<-aov(y~a*b) / running
Anova(model,type=c("III")). However summary(model) gives the same results

in

both cases. Is this how it is set up?

If you use "type-III" tests in an unbalanced ANOVA, and want to test
sensible hypotheses, you should use an orthogonal row-basis for the 
effects,
such as is provided by contr.helmert, contr.poly, or contr.sum, but not by
the default contr.treatment. When you fit a model before changing the
contrast type, contr.treatment is used. Changing the contrast type
subsequent to that has no effect on a model that's already fit (how could
it, unless, e.g., the model is updated?). Because the summary method for 
aov
objects reports "typei-I" (sequential) tests, the results are independent 
of
the contrast type.

Regards,
 John

local({pkg <- select.list(sort(.packages(all.available = TRUE)))

+ if(nchar(pkg)) library(pkg, character.only=TRUE)})

options(contrasts=c("contr.helmert","contr.poly"))
model2<-aov(tdrate~temp*sex)
summary(model2)

             Df   Sum Sq  Mean Sq   F value  Pr(>F)
temp          3 0.110137 0.036712 1005.6947 < 2e-16 ***
sex           1 0.000141 0.000141    3.8593 0.05095 .
temp:sex      3 0.000154 0.000051    1.4073 0.24206
Residuals   187 0.006826 0.000037
---
Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1

Anova(model2,type=c"III")

Error: unexpected string constant in "Anova(model2,type=c"III""

Anova(model2,type=c("III"))

Anova Table (Type III tests)

Response: tdrate
             Sum Sq  Df    F value  Pr(>F)
(Intercept) 0.57549   1 15764.9249 < 2e-16 ***
temp        0.08571   3   782.6314 < 2e-16 ***
sex         0.00023   1     6.2851 0.01303 *
temp:sex    0.00015   3     1.4073 0.24206
Residuals   0.00683 187
---
Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1

--
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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