Journal of Mathematics and Statistics

On Three-Way Unbalance Nested Analysis of Variance

Smaila S. Sanni and Eugene C. Ukaegbu

DOI : 10.3844/jmssp.2012.1.14

Journal of Mathematics and Statistics

Volume 8, Issue 1

Pages 1-14


Problem statement: In this study, we give a simple analytically tractable procedure for solving three-way unbalanced nested Analysis of Variance (ANOVA). In many realistic situations, unbalanced design was unavoidable due to natural constraints and missing data. Approach: Here, we present a comprehensive approach for addressing solutions of problems arising from unbalanced nested ANOVA. We consider the F-statistics under the different models. Results: Special attention was given to the construction of approximate F-test where exact F-test does not exist. Pseudo-degrees of freedoms were derived using the Satterthwaite’s type approximation. Conclusion: In all derivations, we assume that the effects act independently and that the mean squares are independent. A numerical example is given to illustrate the solution procedure.


© 2012 Smaila S. Sanni and Eugene C. Ukaegbu. This is an open access article distributed under the terms of the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original author and source are credited.