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 exactRankTests.
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.
Knut (Ex-G�ttinger)
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 Universit�t 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) [EMAIL PROTECTED] http://www.rucares.org/clinicalresearch/dept/biometry/
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