Science and Education Publishing American Journal of Applied Mathematics and Statistics 2333-4576 2 4 2014 08 07 A-Optimal Split Plot Design for Estimating Variance Components 235 238 EN Nuga O.A Department of Physical Sciences, Bells University of Technology, Ota, Nigeria Amahia G.N Fakorede A AJAMS20142411 10.12691/ajams-2-4-11 2014 06 16 2014 07 07 2014 08 07 We study A-Optimal Split Plot designs for the maximum likelihood estimators of variance components. The work used the general linear model with one whole plot factor and one sub-plot factor and assumed that both factor effects are random variables. Candidates designs with the same number and sizes of whole plot were assigned to the level of the whole plot factor in such a way that formed a balanced one way design. Using the variances of the maximum likelihood estimator of the variance components, candidates designs were compared for A- optimality. The work introduced a method of classifying the five variance components to make comparison and presentation meaningful. The resulting optimal designs depend on the true proportional value of the variance components.