Efficient augmented block designs for unreplicated test treatments

Abstract

Augmented block designs for unreplicated test treatments are investigated under the A- and MV-criteria with respect to control versus control, test versus test and control versus test comparisons. We derive design-independent lower bounds on these criteria over a wide class of competing designs. These bounds are useful benchmarks and the resulting expressions for efficiencies enable objective assessment of any given design under the A- and MV-criteria. It is seen that the use of BIB or PBIB designs or duals thereof often leads to very high efficiencies, which compare extremely well with algorithmic constructions. Our findings also cover the case of partial replication of some test treatments. Illustrative examples, including large-scale ones, are presented.