OCDs in Group Divisible Design Set-Up

Abstract

Optimum covariate designs in simple set-ups such as CRD, RBD and some series of BIBD have already been considered. BIBDs do not exist for many parametric combinations. So there is a need to consider other block designs different from the BIBDs suitable for desired parametric combinations. In this chapter, OCDs have been considered for the less-restrictive set-ups of partially balanced incomplete block designs (PBIBD), which are popular among practitioners. As in the case of BIBDs, the OCDs depend much on the methods of construction of the basic PBIBDs. We focus on one well-known subclass of two-associate class PBIBDs, viz. group divisible designs (GDDs) and develop OCDs based on the GDDs. As before, different combinatorial arrangements and tools such as orthogonal arrays, Hadamard matrices and different kinds of matrix-products, viz. Khatri-Rao product, Kronecker product, etc., have been conveniently used to construct OCDs with as many covariates as possible. A list of OCDs based on some classes of GDDs available in Clatworthy, Tables of two-associate class partially balanced designs, (1973) is given in the appendix for ready reference.

Appendix

A list of OCDs for suitable subclasses of GDDs , viz. SGDDs , SRGDDs and RGDDs divided as singular (S), semi-regular (SR), regular (R) is given below. These are extracted from the catalogue prepared by Clatworthy (1973 ) and amenable to construction of OCDs. See Dutta et al. (2009, 2010 ) in this context. In the constructional method column, T stands for Theorem and R for Remark (Tables 5.1, 5.2 and 5.3).