Evaluating Univariate, Bivariate, and Multivariate Normality Using Graphical and Statistical Procedures

Abstract

This paper reviews graphical and statistical procedures for evaluating multivariate normality by guiding the reader through univariate and bivariate procedures that are necessary, but insufficient, indications of a multivariate normal distribution. A data set utilizing three dependent variables for two groups provided by George and Mallery (1999) is used to analyze kurtosis and skewness coefficients, Q-Q plots, the Shapiro-Wilk or Kolmogorov-Smirnov statistic, and bivariate scatterplots. A procedure programmed by Thompson (1990) is used to explore multivariate normality by plotting Mahalanobis distances against derived chi-square values in a scatterplot.