Try
library(fortunes); fortune("Type III")
(Try it multiple times as there are two relevant quotes: one is to
http://www.stats.ox.ac.uk/pub/MASS3/Exegeses.pdf)
I would not expect modern statistics courses to discuss this issue (or
even ANOVA except for historical information), as with an interactive
computing system you can test any two nested models (and not just linear
Gaussian models). It relates to the mindset of batch-mode packages like
SAS of the 1960s, and seemed old-fashioned even when I first taught the
area in 1979 (using GLIM).
For Bill Venables' preferred approach see Chapter 6 of MASS (the book, any
edition).
On Fri, 26 Sep 2008, Stefan Uhmann wrote:
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: [EMAIL PROTECTED] [mailto:[EMAIL PROTECTED]
On
Behalf Of Menelaos Stavrinides
Sent: September-25-08 9:56 PM
To: r-help@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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PLEASE do read the posting guide http://www.R-project.org/posting-guide.html
and provide commented, minimal, self-contained, reproducible code.
--
Brian D. Ripley, [EMAIL PROTECTED]
Professor of Applied Statistics, http://www.stats.ox.ac.uk/~ripley/
University of Oxford, Tel: +44 1865 272861 (self)
1 South Parks Road, +44 1865 272866 (PA)
Oxford OX1 3TG, UK Fax: +44 1865 272595
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