Profiling the Optimality of Connected Incomplete Block Designs of Size (t=9, b=9, k=3, r=3) Through Their Adjacency Matrices.

Abstract

This article extended the six (6) Incomplete Block Designs (IBDs) represented by letters; A, B, C, D, E and F of size proposed by Nguyen, (1994), and included the combinatorial property of design adjacency on them by constructing seventeen (17) additional IBDs namely; G, H, I, J, K, L, M, N, O, P, Q, R, S, T, U, V and W using all the initial blocks in Nguyen’s via the cyclic method and JAVA codes. The concurrence matrices of all the emerging twenty-three (23) IBDs were subjected to combinatorial conformity via their adjacency matrices based on the numbers of “0’s” and “1’s” in the design layouts, which indicates the extent of connectedness of the designs. Designs H, J, N, O, P, Q, and W turned out to be the preferred set of designs based on the design adjacency, as they provided the best choice of treatment combinations in blocks. Therefore, any of the seven identified optimal designs could be of use by experimenters, investigators, or evaluators who seek an efficient design of size in any field experiment, with their experimental layouts, especially when adjacency of blocks as a combinatorial property is of interest to the researcher.