How to Use Tests for Univariate Normality to Assess Multivariate Normality

Abstract

The assumption of multivariate normality (MVN) underlies many important techniques in multivariate analysis. In the past 50 years, over 50 tests of this assumption have been proposed. However, for various reasons, practitioners are often reluctant to address the MVN issue. In this article, several techniques for assessing MVN based on well-known tests for univariate normality are described and suggestions are offered for their practical application. The techniques are illustrated using two previously published sets of real-life data. In one of the examples it is shown that simply testing each of the marginal distributions for univariate normality can lead to a mistaken conclusion.

Key Words:

• Box–Cox procedure
• Kurtosis
• Shapiro–Wilk test
• Skewness