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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