Estimation of the population covariance coefficient for split-plot experiments

Abstract

In this paper the full Maximum Likelihood Estimator is developed for the true covariance coefficient b, to allow covariance adjustments in split-plot experiments when the main and split-plot residual regression coefficients may be assumed to be equal. Intuitively, pooled estimators should produce the most efficient analysis (as compared with the split-plot regression coefficient, which is frequently used to adjust main and split-plot treatment means). The comparison of the MLE against the Cochran and the split-plot estimators has been investigated. The general conclusion is that, from the practical point of view, the full MLE will perform better than the Cochran's and the split-plot estimators. The Likelihood Ratio Test of the hypothesis that the main-plot and split-plot covariance coefficients are equal, together with the relationship between the observed and asymptotic powers is investigated.