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

From: michael watson (IAH-C) <michael.watson_at_bbsrc.ac.uk>
Date: Thu 21 Apr 2005 - 18:51:29 EST

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@stats.ox.ac.uk] Sent: 20 April 2005 16:35
To: michael watson (IAH-C)
Cc: Liaw, Andy; r-help@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.

Only if you respect marginality. The quote Doug gave is based on a longer
paper available at

```--
Brian D. Ripley,                  ripley@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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