Multiple Comparisons Based on Studentized M-Statistics in a Randomized Block Design

Abstract

In a randomized block design, robust versions based on scale-invariant M-statistics are proposed for single-step multiple comparisons procedures discussed by Tukey (1953) and Dunnett (1955). Although the symmetry of the underlying distribution is needed in the asymptotic theory of Huber's M-estimators, the proposed procedures do not demand the symmetry. It is found that the M-procedures are superior to the classical normal theory procedures except the case that an underlying distribution is normal.