ABSTRACT
The assumption of multivariate normality is intrinsic in most statistical methods used for analyzing multidimensional data. The normality assumption is, in general, dubious even in the univariate case. In multivariate setting the assumption is harder to justify since it implies joint normality in addition to marginal normality. Unlike the assumption of univariate normality, tests for which are a part of most of the software packages, the multivariate normality is rarely verified in practice because of paucity of simple and readily available procedures. In this paper we first survey the literature on testing multivariate normality and then variously examine the appropriateness of normality assumptions for some well known data sets, such as Rao’s Cork data, Fisher’s Iris data, used for illustrative purposes in such leading multivariate analysis monographs as Seber (1984), Anderson (1984) and Mardia (1994). It is seen that, under such scrutiny, the support for multivariate normality for these data is at best equivocal. Hence, in general, such an assumption may be inappropriate and may essentially be illusory. The results emphasize the need for robust multivariate methods.
