[R-sig-eco] R-sig-ecology Digest, Vol 35, Issue 10

[Romain.Piault]

Dear Philip,

thanks a lot for your answer!
I am going to have a look at the reference you propose and see how my
data fulfilled the assumptions if the Hotelling's T-square.

Best regards,

Romain


On Wed, 2011-02-16 at 12:00 +0100, r-sig-ecology-request at r-project.org
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>    1. Hotelling's T-square test (Philip Dixon)
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> ----------------------------------------------------------------------
> 
> Message: 1
> Date: Tue, 15 Feb 2011 07:10:47 -0600
> From: Philip Dixon <pdixon at iastate.edu>
> To: "r-sig-ecology at r-project.org" <r-sig-ecology at r-project.org>
> Subject: [R-sig-eco] Hotelling's T-square test
> Message-ID: <4D5A7B57.4020304 at mail.iastate.edu>
> Content-Type: text/plain
> 
> Romain,
> 
> The numbers of samples have nothing to do with the applicability of 
> Hotelling-s t-square.
> 
> If you believe the underlying populations are multivariate normal *with 
> the same variance-covariance* *matrix*, T-square is an appropriate 
> test.  The assumption of equal VC matrices is more stringent than the 
> univariate assumption of equal variance.  For the multivariate test, the 
> two populations are also assumed to have the same shapes.  My experience 
> is that same shape is often an issue.
> 
> Which approach to use?
> 1) what question do you want to ask?  Do the populations have the same 
> mean vectors? Or, do you want to identify which Y component differs?  
> Either approach answers the first question, although I believe T-square 
> has slightly higher power than multiple testing adjusted t-tests.  
> Univariate t-tests answer the second.
> 2) How strongly do you believe in multivariate normality, especially the 
> same shape part of that assumption?
> 
> Fran James and Chuck McCulloch wrote a very nice summary of multivariate 
> statistics in ecology for Annual Reviews in 1990.  It's old but much of 
> the advice is still relevant.  Much of my thinking on the choice of test 
> is based on their paper.
> 
> Best wishes,
> Philip Dixon
> 
> 
> 
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