Re: [R] Nested ANOVA with covariate using Type III sums of squares

From: Joris Meys <>
Date: Fri, 04 Jun 2010 01:59:50 +0200

Hi Anita,

I have to correct myself too, I've been rambling a bit. Off course you don't delete the variable out of the interaction term when you test the main effect. What I said earlier didn't really make any sense.

That testing a main effect without removing the interaction term is has a tricky interpretation. By removing a main effect you test full model A + B + A:B against the model A + A:B. If you remove the main effect "Zoop" for example, you basically nest Zoop within Diversity and test whether that's not worse than the full model. This explains it very well:

I'd go for type II, but you're free to test any hypothesis you want.


On Thu, Jun 3, 2010 at 9:59 PM, Anita Narwani <>wrote:

> Thanks for your response Joris.
> I was aware of the potential for aliasing, although I thought that this was
> only a problem when you have missing cell means. It was interesting to read
> the vehement argument regarding the Type III sums of squares, and although I
> knew that there were different positions on the topic, I had no idea how
> divisive it was. Nevertheless, Type III SS are generally recommended by
> statistical texts in ecology for my type of experimental design.
> Interestingly, despite the aliasing, SPSS has no problems calculating Type
> III SS for this data set. This is simply because I am entering a co-variate,
> which causes non-orthogonality. I would be happier using R and the default
> Type I SS, which are the same as the Type III SS anyway when I omit the
> co-variate of Mean.richness, except that these results are very sensitive to
> the order in which I add the variables into the model when I do enter the
> co-variate. I understand that the order is very important relates back to
> the scientific hypothesis, but I am equally interested in the main effects
> of Zoop, Diversity, and the nested effect of Phyto, so entering either of
> these variables before the other does not make sense from an ecological
> perspective, and because the results do change, the order cannot be ignored
> from a statistical perspective.
> Finally, I have tried using the Type II SS and received similar warnings.
> Do you have a recommendations?
> Anita.

Joris Meys
Statistical Consultant

Ghent University
Faculty of Bioscience Engineering
Department of Applied mathematics, biometrics and process control

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