Univariate Normal Distribution

Synonyms

Gaussian distribution; Normal distribution

Definition

The normal distribution is a widely used probability distribution to describe samples, populations, and sampling distributions of statistics.

Description

In most of the inferential statistical analyses, one of the important assumptions is the assumption of multivariate normality. Multivariate normality is the assumption that each variable and all linear combinations of the variables are normally distributed (Tabachnick & Fidell, 2007, p. 78). When this assumption is violated, results derived from statistical analysis may not be reliable and valid. For example, multivariate normality of ordinal variables is a condition for the testing of measurement invariance or construct equivalence using the maximum likelihood estimation method of multiple-group confirmatory factor analysis (Byrne, 1998: Koh & Zumbo, 2008). Tests for checking multivariate normality are overly sensitive, and hence, researchers are encouraged to check for...