Usage of Multidimensional Scaling Technique for Evaluating Performances of Multivariate Normality Tests

Abstract

This simulation study has been conducted to evaluate the performances of six different multivariate normality tests under different experimental conditions. Obtained results of 50,000 Monte Carlo Simulation showed the most reliable when the Royston (Roy), Srivastava-Hui (S-H), and Doornik-Hansen test (D-H) have been applied. The above mentioned tests retained Type I error rates at nominal alpha level (0.05). Whereas, the estimations of Type I error of Mardia’s Skewness (M-S), Mardia’s Kent (M-K) and Henze and Zirkler (H-Z) test caused variations depending on sample size and number of variables. The estimations of test power of all tests have been affected by distribution shape, and the all related tests produced highly test power values especially when samples were taken from Multivariate Cauchy and Lognormal distributions. On the other hand, the estimations of test power of all tests have been found extremely low when samples were taken from multivariate t-distribution with 10 d.f. Multidimensional Scaling (MDS) technique has been applied to classify the tests those have had similar performance and the factors those affected the performances of the above mentioned tests. At the end of Multidimensional Scaling analyses, it has been observed that the Roy, S-H and D-H tests showed similar performance, and the performances of these tests were obviously different than that of the others in general.