[R] kruskal wallis for manova?

Knut M. Wittkowski kmw at mail.rockefeller.edu
Fri Nov 21 17:37:25 CET 2003


All linear rank tests, including the Kruskal-Wallis test, can be applied to 
multivariate data, provided that all the variables have the same 
orientation as an underlying unmeasurable (latent) factor. You score the 
multivariate observations first and then treat them as described in Hajek 
and Sidak (1967) for linear rank tests in general, using the R package 

Of course, you wouldn't want to use a (parametric) scoring mechanism, such 
as average z-scores, with a non-parametric test. A unique non-parametric 
scoring system was based on the marginal likelihood principle (Wittkowski 
1992, JASA 75:258). With u-statistics (Wittkowski, in press, Statistics in 
Medicine) one obtains a very good approximation to these unique scores, 
which is computationally more efficient (n^2 vs n!).

Please feel free to contact me for reprints and details.


At 10:29 2003-11-21 -0500, Thomas W Blackwell wrote:
>Nicolaas  -
>I do not know of a multivariate equivalent to the
>(univariate) Kruskal Wallis Rank Sum test, . . .  and
>it's not clear to me that there is a unique way to define
>the ranks for multivariate data in the first place.
>-  tom blackwell  -  u michigan medical school  -  ann arbor  -
> > On Fri, 21 Nov 2003, Nicolaas Busscher wrote:
> >
> > > Hello,
> > > Is there like the kruskal wallis test in relation to ANOVA (no
> > > restrictions on normallity and variance homogenity) something (in R)
> > > for MANOVA?
> > > thanks
> > > --
> > > Dr. Nicolaas Busscher Universität GH Kassel
> > > Nordbahnhofstrasse: 1a, D-37213 Witzenhausen
> > > Phone: 0049-(0)5542-98-1715, Fax: 0049-(0)5542-98-1713

Knut M. Wittkowski, PhD,DSc
The Rockefeller University, GCRC
Experimental Design and Biostatistics
1230 York Ave #121B, Box 322, NY,NY 10021
+1(212)327-7175, +1(212)327-8450 (Fax)
kmw at rockefeller.edu

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