Examining Normality in Incomplete Data Sets: A Note on a Multiple Testing Approach

Abstract

A multiple testing procedure for examining the assumption of normality that is often made in analyses of incomplete data sets is outlined. The method is concerned with testing normality within each missingness pattern and arriving at an overall statement about normality using the available data. The approach is readily applied in empirical research with missing data using the popular software Mplus, Stata, and R. The procedure can be used to ascertain a main assumption underlying frequent applications of maximum likelihood in incomplete data modeling with continuous outcomes. The discussed approach is illustrated with numerical examples.

Keywords:

• incomplete data
• maximum likelihood
• missing at random
• normality

ACKNOWLEDGMENTS

Thanks are due to P. D. Allison and S. Penev for valuable discussions on missing data analysis, as well as to an anonymous referee for critical comments on an earlier version of the article that led to its improvement.

Notes

¹ Use of the Doornik–Hansen (2008) multivariate normality test on the original 100 complete cases in the first example plus the added 10 contaminating complete cases comprising the last pattern of missingness, before missing values were introduced for any of these two sets, was found to be also associated with a p value of .0000 for the ensuing set of 110 complete cases. This finding indicates nonnormality of the 10-variable distribution in that data set, as a result of adding those 10 contaminating cases to the initially considered 100 in this group (representing subsequently the last pattern of missingness). The second example in this illustration section should not be interpreted as implying (a) that the method used here will always sense any violation of normality in a pattern of missingness, in case of such violation; or (b) that the method will always locate correctly the pattern(s) with violation of normality then (see the conclusion).