mixed model nested ANOVA (part two)

Also i have read in Quinn and Keough 2002, design and analysis of
experiments for
biologists, that a variance component analysis should only be conducted
after a rejection
of the null hypothesis of no variance at that level.

Hmmm...

This does rather assume that 'no significant result' means 'near-zero variance contribution'.

These are not identical statements if the anova has low power; an 'insignificant' term can conceal practically important sizes of effect. So if you have a smallish number of groups (say, ten or less) you might want to find out what that estimated between-group variance could have been before you throw it away. That's especially important if you're expecting to say something about standard errors or confidence intervals of fixed effects. 

I may well be biased, here, though. In the kinds of nested design I get involved in (often inter-laboratory or homogeneity studies in chemistry), there is nearly always a between-group  effect; the only question is its size. Under those circumstances, the null hypothesis is not a particularly compelling starting point.  I'd rather have a variance component estimate and know how vague it was than assume it wasn't there at all.

But if you have good power and a good reason for believing there's no case to answer, sure; assume zero unless proven otherwise.

S


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