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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