Discordancy Tests for Outlier Detection in Multi-Item Questionnaires

Abstract

The sensitivity and the specificity of four outlier scores were studied for four different discordancy tests. The outlier scores were the Mahalanobis distance, a robust version of the Mahalanobis distance, and two measures tailored to discrete data, known as O+ and G+. The discordancy tests were Tukey’s fences (a.k.a. boxplot). Tukey’s fences with adjustment for skewness (adjusted boxplot), the generalized extreme studentized deviate (ESD), and the transformed ESD (ESD-T). Outlier scores O+ and G+ performed better than the Mahalanobis distance and its robust version. Discordancy tests ESD-T and adjusted boxplot were advocated for high specificity and ESD for high sensitivity.