[R] Anova - adjusted or sequential sums of squares?

[michael watson (IAH-C)]

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