[R] mahalanobis confusion

[John Fox]

Dear Clayton

At 12:33 PM 1/3/2002 -0800, you wrote:

>My understanding of Mahalanobois distance is that when calculating the 
>distance
>between a vector and the origin should be the same as the absolute value 
>of that
>vector and the origin.
>
>Apparently they are different:

In general, they *are* different: Suppose that x1 and x2 are highly 
positively correlated with 0 means and the same standard deviation. Then 
the generalized distance between (1,1) and the origin will be much smaller 
than between (-1,1) and the origin, since the former is along the major 
axis of the data ellipse. (In contrast, the ordinary Euclidean distances 
are the same.)

Does that help?
  John

-----------------------------------------------------
John Fox
Department of Sociology
McMaster University
Hamilton, Ontario, Canada L8S 4M4
email: jfox at mcmaster.ca
phone: 905-525-9140x23604
web: www.socsci.mcmaster.ca/jfox
-----------------------------------------------------

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