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 D0 D1 D2 and D3 in unbalanced data, and compared them with Type-III sum of squares. Statistics D1 and D2 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, D1 produced power rates higher than Type-III sum of squares. For multiply imputed datasets D1 and D2 may be the best methods for pooling the results in multiply imputed datasets, and for unbalanced data, D1 might be a good alternative to Type-III sum of squares regarding the interaction.