-------- Original Message -------- Subject: Re: regression of Procrustes coordinates on classifiers Date: Fri, 27 Feb 2009 12:41:42 -0800 (PST) From: R.S. Corruccini <[email protected]> To: [email protected] References: <[email protected]>
My first comment is about using Mahalanobis D as a 'distance'. That is really a misnomer. Mahalanobis D is a sum of independent F-tests when you look at how it is calculated. The true distance is perhaps the mean Euclidean distance and Mahalanobis D is the test of whether that Euclidean Distance is actually significantly different from zero. Using Mahalanobis D as a distance is like using a t-test value as a measure of a difference-of-interest.
I don't believe this is correct. t-statistics get larger as n gets larger (if all other things stay the same) but that is not necessarily true of D -- rather, the F statistic derived from D gets larger with larger n.
remember that F-tests explode (they are ratios of squares so if the denominator is unstable the explosion is greater) when the the null hypothesis is not true!
So use the square root -- as is already the case in using D rather than D squared -- RSC -- Robert S. Corruccini Professor and Distinguished Scholar Anthropology Dept. Southern Illinois University Carbondale, Il 62901-4502 -- Replies will be sent to the list. For more information visit http://www.morphometrics.org
