Detecting outliers in multivariate data while controlling false alarm rate

Abstract

Outlier identification often implies inspecting each z-transformed variable and adding a Mahalanobis D2 . Multiple outliers may mask each other by increasing variance estimates. Caroni & 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, α = .05. Simulations studies here compare the single multivariate approach to "multiple-univariate plus multivariate" tests, each at a Bonferroni corrected α 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. The