https://stat.ethz.ch/mailman/listinfo/r-sig-ecology
or, via email, send a message with subject or body 'help' to
r-sig-ecology-request at r-project.org
You can reach the person managing the list at
r-sig-ecology-owner at r-project.org
When replying, please edit your Subject line so it is more specific
than "Re: Contents of R-sig-ecology digest..."
Today's Topics:
1. Hotelling's T-square test (Philip Dixon)
----------------------------------------------------------------------
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
[[alternative HTML version deleted]]
------------------------------
_______________________________________________
R-sig-ecology mailing list
R-sig-ecology at r-project.org
https://stat.ethz.ch/mailman/listinfo/r-sig-ecology
End of R-sig-ecology Digest, Vol 35, Issue 10
*********************************************