[R] Anova - adjusted or sequential sums of squares?
michael watson (IAH-C)
michael.watson at bbsrc.ac.uk
Thu Apr 21 10:51:29 CEST 2005
OK, I had no idea I was opening such a pandora's box, but thank you for
all of your answers, it's been fascinating reading.
This is how far I have got:
I will fit the most complex model, that is the one that includes the
interaction term. If the interaction term is significant, I will only
interpret this term.
If the interaction term is not significant, then it makes sense to test
the effects of the factors on their own. This is where I get a little
shaky... Using the example from the WNV paper, page 14. If I want to
test for the effect of Litter, given that I have already decided that
there is no interaction term, I can fit:
Wt ~ Mother + Litter
Wt ~ Litter + Mother
Wt ~ Litter
The latter tests for the effect of Litter ignoring the effect of Mother.
The first two test for the effect of Litter eliminating the effect of
Mother. Have I read that correct? However, it still remains that the
top two give different results due to the non-orthogonal design.
The way I see it I can do a variety of things when the interaction term
is NOT significant and I have a non-orthogonal design:
1) Run both models "Wt ~ Mother + Litter" and "Wt ~ Litter + Mother" and
take the consensus opinion. If that's the case, which p-values do I use
in my paper? (that's not as flippant a remark as it should be...)
2) Run both models "Wt ~ Litter" and "Wt ~ Mother", and use those. Is
that valid?
3) Believe Minitab, that I should use type III SS, change my contrast
matrices to sum to zero and use drop1(model, .~., test="F")
Many thanks
Mick
-----Original Message-----
From: Prof Brian Ripley [mailto:ripley at stats.ox.ac.uk]
Sent: 20 April 2005 16:35
To: michael watson (IAH-C)
Cc: Liaw, Andy; r-help at stat.math.ethz.ch
Subject: RE: [R] Anova - adjusted or sequential sums of squares?
On Wed, 20 Apr 2005, michael watson (IAH-C) wrote:
> I guess what I want to know is if I use the type I sequential SS, as
> reported by R, on my factorial anova which is unbalanced, am I doing
> something horribly wrong? I think the answer is no.
Sort of. You really should test a hypothesis at a time. See Bill's
examples in MASS.
> I guess I could use drop1() to get from the type I to the type III in
> R...
Only if you respect marginality. The quote Doug gave is based on a
longer
paper available at
http://www.stats.ox.ac.uk/pub/MASS3/Exegeses.pdf
Do read it all.
--
Brian D. Ripley, ripley at stats.ox.ac.uk
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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