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Subject: Mahalanobis significance tests
From: Dean Jerry <[log in to unmask]>
Reply-To:Academic forum on fisheries ecology and related topics <[log in to unmask]>
Date:Tue, 27 May 1997 11:11:30 +1000

text/plain (44 lines)

Hi all,

I have a statistical problem that I can't resolve.  I have measured
morphometric variabilty in populations of Australian bass from seven locales
throughout this species range.  Both univariate and multivariate tests
indicate that the collections exhibit significant  morphological variation.
From a discriminant function analysis I have derived pairwise Mahalanobis
squared distances between locales and now want to test to see which
collection centroids indicated by these squared distances are significantly
different.  After much searching I have come up with an F-test reputed to
test these distances.  The only problem is that the authors neglected to
mention what one of the symbols in the equation means.  Can anybody suggest
what the p in the following equation relates to?  I suspect it is the number
of variables entered into the discriminant function but I am not sure.  The
equation is:

        F (p, n - g - p + 1) = D2  *  (1/nA + 1/nB)-1 *  (n - p - 1)/p (n -
g),  where D2 is Mahalonobis squared distance, nA is the number of
observations in collection A, n is the total number of observations, and g
is the number of groups.  This F-test comes from

         J.M. McGlade and E.G. Boulding. 1986. The truss: A geometric and
statistical approach to the analysis of form in fishes.          Canadian
Technical Report of Fisheries and Aquatic Sciences No 1457.

Thanks in advance,

Dean Jerry
Dean Jerry
Animal Conservation Genetics
Southern Cross University
NSW 2480
Ph: 61 66 203815
Fax: 61 66 212669
If we possessed a thorough knowledge of all parts of the seed of any
animal, we could from that alone, by reasons entirely mathematical and
certain, deduce the whole conformation and figure of each of its members,
and, conversely if we knew several peculiarities of this conformation, we
would from those deduce the nature of its seed.
Rene` Descartes 1596-1650 (Oeuvres iv, 494)

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