Design issues related to allocation of experimental units with known covariates into two treatment groups

An experimental situation corresponding to an ANCOVA model involving several known covariates is of interest in many practical situations related to various disciplines. The design problem here is to determine an optimal allocation rule for the experimental units with known covariate(s) into two treatments such that both treatment and covariate effects, or only treatment effect, are efficiently estimated in terms of the commonly used DD- or AA-optimalities. The present work deals with development of a new allocation algorithm for this purpose. The algorithm generates efficient allocation in comparison to random allocation and allocation designs already reported in the literature. At the same time the algorithm requires less computational work. With large number of experimental units and several covariates, the exact optimal allocation is computationally intractable. In such situation, we have proposed an algorithm for finding a near-optimal allocation design that is motivated by computationally tractable optimization technique. Through simulation experiments and real life data analysis, we have demonstrated the efficiency of the proposed algorithm.