Abstract: 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.