Analysis of Variance for Three-Way Unbalanced Mixed Effects Interactive Model

In the study, a method of solving ANOVA problems based on an unbalanced three-way mixed effects model with interaction for data when factors A and B are fixed, and factor C is random was presented, and the required EMS was derived. Under each of the appropriate null hypotheses, it was observed that none of the derived EMS was unbiased for the other. Unbiased estimators of the mean squares were determined to test hypotheses. With the unbiased estimators, appropriate F-statistics as well as their corresponding pseudo-degrees of freedom were obtained. The theoretical results presented in the paper were illustrated using a numerical example.