[R] MANOVA power, degrees of freedom, and RAO's paradox

[Prof Brian Ripley]

R's manova is not intended to handle `nested unbalanced data': it
cross-references ?aov, which says the unbalanced part, and ?manova says
the nested part.

On Mon, 5 Jan 2004, Oliver Bossdorf wrote:

> Hi,
> 
> I have a nested unbalanced data set of four correlated variables. When I 
> do univariate analyses, my factor of interest is significant or 
> marginally significant with all of the variables. Small effect size but 
> always in the same direction. If I do a MANOVA instead (because the 
> variables are not independent!) then my factor is far from being 
> significant. How does that come about?
> 
> I have found a mention of a so-called Rao's paradox, which seems to deal 
> with exactly this phenomenon. Does anyone know more about it, e.g. a 
> reference?
> 
> The next strange thing is that if do the MANOVA in R, then both 
> hypothesis and error degrees of freedom are multiplied by the number of 
> variables. When I do it in SAS, however, only the hypothesis d.f. are 4 
> x univariate, while the error d.f. are as in univariate, minus 3. This 
> is irritating, in particular since no indication is given in the 
> handbooks as to how degrees of freedom are calculated in a MANOVA? Can 
> anyone tell me more about this? Are there different philosphies that are 
> responsible for the differences between R and SAS?
> 
> I would be grateful for any help.
> 
> Regards, Oliver
> 
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-- 
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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