When conducting a structural equation model (SEM) or confirmatory factor analysis (CFA), it is often recommended to test for multivariate normality. Some popular SEM software packages (such as AMOS) assume your variables are continuous and produce the best results when your data are normally distributed. Here we discuss a few options for testing normality in SEM.
First, researchers can test for multivariate normality using a quantile (Q-Q) or probability (P-P) plot in SPSS through the Analyze > Descriptive Statistics menu. They can also create a quantile plot of Mahalanobis distances to check for normality. SPSS provides steps for calculating Mahalanobis distances, while Intellectus Statistics performs this method automatically. In all cases, the plot should show points following a relatively straight line. Marked deviations from a straight line suggest that the data are not multivariate normal.
In AMOS, the built-in normality test calculates Mardia’s coefficient, a multivariate kurtosis measure. AMOS provides this coefficient and a critical value for significance testing. A critical value of 1.96 corresponds to a p-value of 0.05. If Mardia’s coefficient is significant (critical ratio > 1.96), the data may not follow a normal distribution. However, this significance test on its own is not a practical assessment of normality, especially in SEM. These tests are highly sensitive to sample size. Larger samples are more likely to produce significant (non-normal) results.
In SEM, where your sample size is expected to be very large, this means that Mardia’s coefficient is almost always guaranteed to be significant. Thus, the significance test on its own does not provide very useful information. Researchers should use significance tests along with descriptive statistics, such as kurtosis values for individual variables (Stevens, 2009). Kurtosis values greater than 3.00 may indicate non-normal distribution (Westfall & Henning, 2013).
Researchers use many methods to test for normality, and SEM analysis use the most popular ones.
References
Stevens, J. P. (2009). Applied multivariate statistics for the social sciences (5th ed.). Mahwah, NJ: Routledge Academic.
Westfall, P. H., & Henning, K. S. S. (2013). Texts in statistical science: Understanding advanced statistical methods. Boca Raton, FL: Taylor & Francis.