>> 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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