Comparing Tests of Multinormality - A Monte Carlo Study

by Alexander von Eye.

Abstract: Multivariate statistical methods often require the assumption of multivariate normality. The purpose of this study was to compare four tests of multinormality and to answer questions concerning their sensitivity to various data characteristics. The four comparison tests are Mardias tests of multivariate skewness and kurtosis and von Eye et al.s sector and overall tests. The five factors included in the Monte Carlo study were sample size, number of variables, five types of distributions (normal, uniform, logarithmic, inverse Laplace transformed, and cube root transformed), magnitude of correlation among variables, and the number of segments used for the ?2 tests. Results suggest (1) that the type of distribution has the strongest effect on whether the tests indicate violations of the multinormality assumption, (2) the Mardia tests are sensitive in particular to the violations they were designed to detect, and (3) the new tests by von Eye et al. are omnibus to all violations included in the simulations. Implications are discussed.

Key Words: Mardia's skewness and kurtosis, von Eye's sector tests, sensitivity, omnibus tests

Author:
Alexander von Eye, voneye@msu.edu

Editor: Richard G. Graf, rgraf@sunstroke.sdsu.edu

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