[R] MANOVA power, degrees of freedom, and RAO's paradox
Oliver Bossdorf
oliver.bossdorf at ufz.de
Mon Jan 5 13:30:25 CET 2004
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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