Multiple imputation to balance unbalanced designs for two-way analysis of variance

Abstract

A balanced ANOVA design provides an unambiguous interpretation of the F-tests, and has more power than an unbalanced design. In earlier literature, multiple imputation was proposed to create balance in unbalanced designs, as an alternative to Type-III sum of squares. In the current simulation study we studied four pooled statistics for multiple imputation, namely D-0, D-1, D-2, and D-3 in unbalanced data, and compared them with Type-III sum of squares. Statistics D-1 and D-2 generally performed best regarding Type-I error rates, and had power rates closest to that of Type-III sum of squares. Additionally, for the interaction, D-1 produced power rates higher than Type-III sum of squares. For multiply imputed datasets D-1 and D-2 may be the best methods for pooling the results in multiply imputed datasets, and for unbalanced data, D-1 might be a good alternative to Type-III sum of squares regarding the interaction.