Optimum Choice of Covariates for a Series of SBIBDS Obtained Through Projective Geometry

Abstract

A block design set up is considered in presence of a number of controllable covariates. The problem is that of choosing the values of the covariates so that for a given block design, it is optimum in the sense of attaining minimum variance for the estimation of each of the covariate parameters. In case of incomplete block designs, the choice of the values of the covariates depends heavily on the allocation of treatments to the plots of blocks; more specifically on the method of construction of the incomplete block design. In this paper the situation where the block design is a member of the complementary series of balanced incomplete block design (BIBD) with parameters b = v = sN+sN-1+…+s+1, r = k = sN, λ=sN-sN-1 of symmetric balanced incomplete block design (SBIBD) obtained through projective geometry is considered. AMS Subject Classification: Primary 62K05; Secondary 62K10.