Detecting outliers in multivariate data while controlling false alarm rate

Outlier identification often implies inspecting each z-transformed variable and adding a Mahalanobis D^2. Multiple outliers may mask each other by increasing variance estimates. Caroni and Prescott (1992) proposed a multivariate extension of Rosner s (1983) technique to circumvent masking, taking sample size into account to keep the false alarm risk below, say, alpha = .05. Simulations studies here compare the single multivariate approach to "multiple-univariate plus multivariate" tests, each at a Bonferroni corrected alpha level, in terms of power at detecting outliers. Results suggest the former is better only up to about 12 variables. Macros in an Excel spreadsheet implement these techniques.