On Probability Plot Correlation Coefficient Test for Multivariate Normality

Abstract

A basic graphical approach for checking normality is the Q-Q plot that compares sample quantiles against the population quantiles. In the univariate analysis, the probability plot correlation coefficient test for normality has been studied extensively. We consider testing the multivariate normality by using the correlation coefficient of the Q-Q plot. When multivariate normality holds, the sample squared distances should follow a chi-square distribution. The plot should resemble a straight line. A table of critical points for the probability plot correlation coefficient test for multivariate normality is constructed by simulation. The probability plot correlation coefficient test alone does not guarantee multivariate normality. So we use the following two steps to test multivariate normality. First, we check the multivariate normality by the probability plot correlation coefficient test. If the test does not reject the null hypothesis, then we test symmetry of the distribution and determine whether multivariate normality holds. The size and power of this testing procedure are studied.