MANOVA power, degrees of freedom, and RAO's paradox
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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