Plotting Bivariate Normal Data

From: Berton Gunter
 
Just a little addendum to Martin's comments below. It is well 
known that
using LS centers and covariances for the M-distances is 
generally not a good
way to do this, as these statistics, themselves, are 
distorted by the long
"tails" (do > 1D distributions have "tails"?) 

so that the problems are
hidden (see Brian Ripley's comments on the R-Help "robust 
regression with
groups" thread  from last week). Hence, one should use a 
resistant center
(the medioid, say) and a resistant covariance matrix (e.g., 
from cov.rob())
to compute the M-distances.

... But then, this begs the question: Why do normality testing at all?
(again, see BR's comments). Better to use robust/resistant statistical
procedures for estimation from the beginning, though, 
unfortunately, this
shatters the nice simple mathematical framework for inference. 

-- Bert Gunter
Genentech Non-Clinical Statistics
South San Francisco, CA
 
"The business of the statistician is to catalyze the 
scientific learning
process."  - George E. P. Box
 
 

Since one of the more severe and common deviations from
normality is "long tailed"ness (in all it's vaguety), we have
been recommending to QQ-plot mahalanobis distances against chi
squared quantiles - even before looking at the univariate
QQ plots.

Exactly for this reason, in R,
	example(mahalanobis)
shows a version of how to do this!

Martin Maechler, ETH Zurich