A-optimality of Group Divisible Designs with Unequal Block Sizes for Making Test Treatments-Control Comparison under a Heteroscedastic Model

Abstract

This paper investigates the problem of obtaining efficient block designs with unequal block sizes for making test treatments-control comparisons under a heteroscedastic model where the intra block variances are assumed to be proportional to certain non-negative integral power of the block sizes.The concept of Group Divisible Treatment Designs is extended to Group Divisible Treatment Designs with unequal block sizes (GDTUB designs) of type G. A sufficient condition is obtained for A-optimality of GDTUB designs of type G in the class of designs which are binary in test treatments and in which the control treatment is added the same number of times to each block of same size and where this is done in at least one set of blocks. Two methods of construction of GDTUB designs of type G are also given. A catalogue of A-optimal designs is prepared. The use of a computer program given in the appendix shows that the designs catalogued are A-optimal in their respective classes even when the designs are non-binary in the test treatments