Research Article Open Access

On Three-Way Unbalance Nested Analysis of Variance

Smaila S. Sanni and Eugene C. Ukaegbu

Abstract

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.

Journal of Mathematics and Statistics
Volume 8 No. 1, 2012, 1-14

DOI: https://doi.org/10.3844/jmssp.2012.1.14

Submitted On: 2 September 2011 Published On: 10 December 2011

How to Cite: Sanni, S. S. & Ukaegbu, E. C. (2012). On Three-Way Unbalance Nested Analysis of Variance. Journal of Mathematics and Statistics, 8(1), 1-14. https://doi.org/10.3844/jmssp.2012.1.14

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Keywords

  • Unbalanced data
  • mean square
  • pseudo-degrees of freedom
  • approximate F-test
  • nested design
  • statistical software
  • least squares method
  • natural barriers
  • linear model
  • model parameters