Comparing Tests of Multinormality under Sparse Data Conditions - a Monte Carlo Study

by Alexander von Eye.

Abstract: Mardia's tests of multivariate skewness and kurtosis and von Eye and Gardiner's and von Eye and Bogat's sector and overall tests of multinormality are compared under sparse data conditions. A Monte Carlo study is reported in which five factors were varied: sample size, number of variables, type of distribution (normal, uniform, log-transformed, inverse Laplace- transformed, and cube root-transformed), magnitude of correlation among variables, and the number of segments used for the 2-tests. Results suggest that, even under sparse data conditions, (1) the Mardia tests are differentially sensitive to the violations they were designed to detect; (2) the new sector and overall tests are sensitive to all violations included in the simulations; (3) the effects of the small samples can be seen in an increased random component of the data structure; and (4) although the overall and the sector tests are still sensitive to a wide range of violations, the test statistics are not always distributed as chi2, due to the well known inflation of X2. These results replicate, in part, the results of von Eye's (2005) study, in which larger samples had been used. However, they also show that sufficiently large samples are needed for valid statistical decisions about multinormality.

Key Words: Mardia's skewness and kurtosis tests; von Eye's sector tests; sparse data; sensitivity

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Editor: Alexander von Eye, voneye@msu.edu

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