Mahalanobis distances were calculated using the mahalanobis R function. Under standard normal theory, these are approximately Chi-squared on 3 degrees of freedom.
A data frame with 21 rows and 2 variates:
Mahalanobis squared distances from the arithemetic mean using the eliptical contours of the sample covariance matrix.
As with distances, these are Mahalobis squared distances butnow based on robust measures of location and covariance matrix (as determined from the default covRob of the robust package).
with(stacklossDistances, qqtest(robust,dist="chi", df=3)) will show "outliers".
with(stacklossDistances, qqtest(ordinary,dist="chi", df=3)) will show "inliers".
"Statistical Theory and Methodology in Science and Engineering", K.A. Brownlee, (1960, 2nd ed. 1965), Wiley, New York pp. 491-500.