A Simple Test for Departures from Multivariate Normality

Patrick Peterson and Arnold J. Stromberg

Abstract:

One of the authors [AS] was recently asked to teach a graduate level applied multivariate methods course. The audience was primarily graduate students in departments other than Statistics who would need to use multivariate statistical methods in their dissertations. As a good teacher of multivariate method should, I stressed the need to verify assumptions when applying any particular statistical method. Surprisingly, at least to me, SAS does not provide a test for multivariate normality.

It is well known that a random vector Y has a multivariate normal distribution if and only if every linear combination of the components of Y has a univariate normal distribution. We discuss a test based on this idea that is reasonably powerful and computationally simple.

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