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.

中文翻译：

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无事生非：多重插补平衡不平衡设计的双向方差分析

在早期的文献中，提出了多重插补以在不平衡设计中创建平衡，作为双向 ANOVA 中 III 型平方和的替代方案。在当前的模拟研究中，我们研究了多重插补的四个汇总统计数据，即不平衡数据中的 D₀、D₁、D₂ 和 D₃，并将这些统计数据与 III 类平方和进行了比较。统计数据 D₀ 和 D₂ 通常在类型 I 错误率方面表现最好，并且具有最接近类型 III 平方和的功率率。然而，没有一个统计数据产生的功率率高于第三类平方和。结果得出的结论是，对于多重插补数据集，D0 和 D2 可能是在多重插补数据集中汇集多参数估计结果的最佳方法，对于不平衡数据，