[R] Random Effects for One-Way Anova

[Prof Brian Ripley]

On Wed, 30 Nov 2005, Peter Dalgaard wrote:

> Prof Brian Ripley <ripley at stats.ox.ac.uk> writes:
>
>>> My questions is:
>>> which formula should I use if I want to use a random effects model?
>>> I think I should use "lme", but I don't know how.
>>
>> aov() is the function for anova modelling. so you want
>>
>> aov(A ~ B, data = DATA)         # fixed effects
>> aov(A ~ Error(B), data = DATA)  # random effects
>>
>> but a 1-way ANOVA with fixed or random effects is the same analysis, and
>> only the interpretation differs.
>
> Not quite. Only if the design is balanced and you're not looking to
> compute things like the variance of the estimated overall mean.

(That's part of the interpretation.  An ANOVA does not give you that.)

> In the unbalanced case, I don't believe aov() is doing the right thing
> (it might not be very wrong, though, if the imbalance is slight) and
> lme/lmer is closer on the mark.

The example given in his follow-up posting was balanced, though.

I think it is pretty conventional to consider such ANOVAs to be balanced, 
and if they are not, to use the term to refer to the classical analyses 
even if they are not according to some definition `the right thing'.

-- 
Brian D. Ripley,                  ripley at stats.ox.ac.uk
Professor of Applied Statistics,  http://www.stats.ox.ac.uk/~ripley/
University of Oxford,             Tel:  +44 1865 272861 (self)
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