A new graphical tests for multivariate normality

A new methodology for assessing distributional assumptions of multivariate data, with graphical applications, is presented. The underlying procedure is based on transforming the multivariate sample into a set of uncorrelated samples and representing the order statistics of each transformed sample by linked vectors in a two dimensional space. The proposed method is described and its properties discussed. The multivariate normality tests are reviewed and a new classification scheme for them is proposed. The new test is then compared with a selection of the ‘best’ competing ones under an exhaustive Monte Carlo study. A selection of ‘best’ tests for several non normal alternatives, with advantages and disadvantages, is given. Graphical aspects of the new procedure are discussed.