Normality - Reasons for Screening Data

Prior to analyzing multivariate normality, one should consider univariate normality

• Histogram, Normal Q-Qplot (values on x axis with expected normal values on the y axis)
• Skewness and Kurtosis (null hypothesis: values around zero with alpha levels of .01 or .001
• Kolmogorov-Smirnov Test

Multivariate normality refers to a normal distribution of combination of variables (two-by-two, plus all linear combination of the variables) Univariate normality is a necessary but not sufficient condition for multivariate normality.

For bivariate normality one should check all the two-by-two scatter plots (they should have elliptical shape)

Sometimes data transformation is necessary for normality.