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.
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