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Re: [S] Multivariate hypothesis tests

To: s-news@wubios.wustl.edu, prechelt@ira.uka.de
Subject: Re: [S] Multivariate hypothesis tests
From: Prof Brian Ripley <ripley@stats.ox.ac.uk>
Date: Wed, 26 Jan 2000 10:48:43 +0000 (GMT)
Reply-to: Prof Brian Ripley <ripley@stats.ox.ac.uk>
Sender: owner-s-news@wubios.wustl.edu

> To: s-news@wubios.wustl.edu
> Subject: [S] Multivariate hypothesis tests
> Date: Wed, 26 Jan 2000 11:14:22 +0100
> From: Lutz Prechelt <prechelt@ira.uka.de>
> X-loop: s-news
> 
> 
> Hi all,
> 
> I am looking for S implementations of multivariate significance
> tests.
> Neither the S-Plus 5 manual, nor VR2, nor statlib appear to have
> any.
> 
> Specifically, I need to test two bivariate samples for 
> a difference in means. Both variables are from continuous
> distributions but one has a strong ceiling effect and the
> other I would rather also not trust to be normally distributed.
> 
> Any hints, please?

Your query presumes that that are standard tests here, and I think there
are not. Suppose you had 20 dimensions. Then how should we compare
the import of differences in different directions?  If we assume normality the 
covariance matrices give us metrics, but in general?

Even in the univariate case _and_ normality you have the Behrens-Fisher
problem which has no universally accepted answer.

Mardia, Kent & Bibby has a reasonable overview of what is known and a
test (by Mardia) for the non-normal bivariate case which might do what you
want.


-- 
Brian D. Ripley,                  ripley@stats.ox.ac.uk
Professor of Applied Statistics,  http://www.stats.ox.ac.uk/~ripley/
University of Oxford,             Tel:  +44 1865 272861 (self)
1 South Parks Road,                     +44 1865 272860 (secr)
Oxford OX1 3TG, UK                Fax:  +44 1865 272595

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