COMPARATIVE STUDY OF OPTIMALITY CRITERIA FOR PARTIALLY BALANCED LATTICE DESIGNS

Partially Balanced Lattice Designs (PBLD) is a subclass of Incomplete Block Designs which are similar to the Balanced Lattices only that they allows for more flexible choice of the number of replications, the PBLD requires that the number of treatments must be a perfect square and that Block size k must be equal to the square root of these treatments number. Balanced Lattice Design require the number of replications to be . They exist for certain parameters. They require large number of replications, which consumes logistics, time and effectiveness. The aim of this study is to compare Optimality Criteria for a Partially Balanced Lattice Designs with three associate classes. The design based of A-, D-, and G- optimality criteria were employed. This approach demonstrated in our study involving thirty-two, fortyeight and sixty-four treatments. The results show that D-optimality has the highest values in all the categories followed by G- and A-optimality criteria respectively, it means that D- criteria is more optimal than A- and G- criteria. In the same manner, the efficiencies of this Design were considered by maximizing the information matrix; the results revealed that A- and Defficiency criteria have the same efficiency and greater than G- criteria in all the categories, D-efficiency Criteria is consider to be the most optimal and most efficient among all the criteria despite having the same efficiencies with A-optimality. Hence, it show that the more, the replication the more the optimal and efficient of the design. It is therefore recommended here that for studies in Partial Lattice Designs, D- Optimality is better. Agricultural researchers, sample surveyors, plant breeders, environmentalists, social scientists as well as medical and health officials should use Partial Lattice Designs to test a large number of entries that are compare directly for selection, it is cost effective in experimental Designs and improve efficiency. It also serves as reference material for researchers who wishes to carryout research on Partial Lattices