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 > > ______________________________________________ > [EMAIL PROTECTED] mailing list > https://stat.ethz.ch/mailman/listinfo/r-help > PLEASE do read the posting guide! > http://www.R-project.org/posting-guide.html > ______________________________________________ [EMAIL PROTECTED] mailing list https://stat.ethz.ch/mailman/listinfo/r-help PLEASE do read the posting guide! http://www.R-project.org/posting-guide.html