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.

Keywords

• unbalanced designs
• multiple imputation
• two-way analysis of variance
• missing data
• type-iii sum of squares