-------- Original Message --------
Subject: RE: Proper use and meaning of Mahalanobis distances
Date: Wed, 20 Feb 2008 10:49:42 -0800 (PST)
From: F. James Rohlf <[EMAIL PROTECTED]>
Reply-To: [EMAIL PROTECTED]
Organization: Stony Brook University
To: [email protected]
References: <[EMAIL PROTECTED]>
The formula for Mahalanobis distance ensures that it _always_ gives a
distance between points relative to variation in the pooled
within-groups covariance matrix used in its computation. It has the same
meaning in a CVA as when one just compares two groups. It is not a
measure of absolute morphological difference but it a measure of how
easy it is to distinguish two groups. Better to think of it as a
statistical distance.
Perhaps not useful to think of it as "correcting" for correlations among
variables - it simply gives one the distance between two groups relative
to the amount of within-group variation in the direction of the
difference between the two groups being compared. (easier to explain if
I could wave my hands around in this message.)
Note also that often the formulas for Mahalanobis distance are actually
formulas for the square of that distance so a square root is often needed.
------------------------
F. James Rohlf, Distinguished Professor
Ecology & Evolution, Stony Brook University
www: http://life.bio.sunysb.edu/ee/rohlf
-----Original Message-----
From: morphmet [mailto:[EMAIL PROTECTED]
Sent: Tuesday, February 19, 2008 3:40 PM
To: morphmet
Subject: Proper use and meaning of Mahalanobis distances
Misdirected post 7 of 7. -mod
-------- Original Message --------
Subject: Proper use and meaning of Mahalanobis distances
Date: Mon, 11 Feb 2008 20:40:19 -0500
From: morphmet <[EMAIL PROTECTED]>
To: morphmet <[EMAIL PROTECTED]>
-------- Original Message --------
Subject: Proper use and meaning of Mahalanobis distances
Date: Mon, 11 Feb 2008 12:17:11 -0800 (PST)
From: [EMAIL PROTECTED]
To: [email protected]
Dear colleauges,
Recently I received comments from a manuscript reviewer regarding the
use of
Mahalanobis distance vs. Euclidean. The reviwer argues that Euclidean
distance
measures the mrophological difference between means, Mahalanobis scales
that
difference by within group variance.
The problem I found with this remark is that Mahalanobis distance can
only be
interpreted in such a way under the context of a discriminant function
or
similar (e.g. CVA). But not in all cases will Mahalanobis distance
expresses
itself as maximizing group differentiation. It does corrects for
variable
correlation, but by no means will it by itself scale distances relative
to
within group variance.
The reviewer is of course anonimous, but I hope he/she can read this.
This issue raised after my comments on the proper use and
interpretation of
discriminant analysis (or similar such as CVA) as evidence for group
separation. I argue that there is no point in using such methods as
evidence
for the existence of groups, since they require the existence of such
groups at
the start. An good example in tautology, and a misleading one since
distances
between groups will always tend to be large, and should not not be
interpreted
as one interprets Euclidean distances in a PCA.
I will appreciate any comments regarding this subject.
Thanks
Pablo
Pablo Jarrin
Dept. of Biology
Boston University
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