Some p-variate adaptations of the shapiro-wilk test of normality

Abstract

The assumption of multivariate normality is a common prac-tice in the analyses of multivariate data. But it is rarely verified, in part, because of the lack of simple and easy to use test proce-dures to detect such violations. In this paper we decompose the problem of testing the hypothesis of multivariate normality into component problems of testing univariate normality. These prob-lems are then solved using the well known W-test due to Shapiro and Wilk (1965). The operating characteristics of the new test procedures are evaluated and compared with Z _p test due to Mud-holkar, McDermott, and Srivastava (1992) and test due to Mardia and Foster (1983). An extensive simulation study demon strates that the new test procedures have excellent type I error control for samples of size as small as 20 and have superior power properties as compared to their competitors.

Keywords:

• Wtest
• marginal normality
• p-values
• combining tests