Estimation and its Precision of Fixed Polynomial Effects of Response Surface Models with Random Block Effects

In this paper, we study the variances of used in mixed design model, and prove that, three estimators of treatment contrast, namely, intra-block estimator and least square estimator and intra-block inter-block combined estimator have the same variances, under the fact that the design block is orthogonal. The study develops A. L. Khuri’s work³ and presents an important theory basement for using orthogonal design in mixed blocks design.