THIS ARTICLE HAS BEEN RETRACTED: Much Ado About Nothing: Multiple Imputation to Balance Unbalanced Designs for Two-Way Analysis of Variance


  • Joost R. van Ginkel
  • Pieter M. Kroonenberg


Retraction(s) for this article:
Methodology, 16(4), 354–355,

A new version is available:
Methodology, 17(1), 39–57,

Original abstract:
In earlier literature, multiple imputation was proposed to create balance in unbalanced designs, as an alternative to Type III sum of squares in two-way ANOVA. In the current simulation study we studied four pooled statistics for multiple imputation, namely D₀, D₁, D₂, and D₃ in unbalanced data, and compared these statistics with Type III sum of squares. Statistics D₀ and D₂ generally performed best regarding Type-I error rates, and had power rates closest to that of Type III sum of squares. However, none of the statistics produced power rates higher than Type III sum of squares. The results lead to the conclusion that for multiply imputed datasets D₀ and D₂ may be the best methods for pooling the results of multiparameter estimates in multiply imputed datasets, and that for unbalanced data, Type III sum of square is to be preferred over using multiple imputation in obtaining ANOVA results.