Analysis of Variance of Multiply Imputed Data

As a procedure for handling missing data, Multiple imputation consists of estimating the missing data multiple times to create several complete versions of an incomplete data set. All these data sets are analyzed by the same statistical procedure, and the results are pooled for interpretation. So far, no explicit rules for pooling F-tests of (repeated-measures) analysis of variance have been defined. In this paper we outline the appropriate procedure for the results of analysis of variance for multiply imputed data sets. It involves both reformulation of the ANOVA model as a regression model using effect coding of the predictors and applying already existing combination rules for regression models. The proposed procedure is illustrated using three example data sets. The pooled results of these three examples provide plausible F- and p-values.