Small Sample Statistics for Incomplete Nonnormal Data: Extensions of Complete Data Formulae and a Monte Carlo Comparison

Incomplete nonnormal data are common occurrences in applied research. Although these 2 problems are often dealt with separately by methodologists, they often cooccur. Very little has been written about statistics appropriate for evaluating models with such data. This article extends several existing statistics for complete nonnormal data to incomplete data and evaluates their performance via a Monte Carlo study. The focus is on statistics that also perform well in small samples. The following statistics are defined and studied: corrected residual-based statistic, residual-based F statistic, scaled chi-square, adjusted chi-square, Bartlett-corrected scaled chi-square, and Swain-corrected scaled chi-square. Both Type I error rates and power are studied with missing completely at random nonnnormally distributed data and varying degrees of nonnormality. Sample size, model size, and number of variables containing missingness are also varied. For power comparisons, both minor and major model misspecifications are considered. Two statistics had the best Type I error control and power: the adjusted chi-square and Bartlett-corrected chi-square. These statistics are recommended to practitioners. It is concluded that model fit can be assessed reliably and with sufficient power even at the intersection of all 3 problems: incomplete data, nonnormality, and small sample size.