A-Optimal Block Designs With Unequal Block Sizes For Comparing Two Disjoint Sets Of Treatments

Abstract

This article studies an experimental setting in which it is desired to compare v1 test treatments with v2 control treatments and the experimental units are arranged in b blocks, where each of the bn blocks contains kh experimental units, h=1,…,p. Under this setting a general algorithm has been developed to generate A-optimal block designs for making such comparisons, when the block sizes are small and also the sizes do not vary widely. As a particular case the algorithm has been obtained when there are two types of block sizes i.e. k1 =2 and k2 = 3. Further a sufficient condition is obtained to establish the A-optimality of designs when there is no restriction on the block sizes. A method of construction of variance balanced designs with unequal block sizes for comparing treatments belonging to two disjoint sets is given. The A-efficiency of the designs constructed is investigated. A catalogue of such designs for two control treatments along with their A-efficiencies is prepared.