Construction of Equireplicate Balanced Incomplete Block Designs with Unequal Block Sizes

Abstract

There are three major concepts of balancing in incomplete block designs viz variance balancing, pair wise balancing and efficiency balancing. The necessary and sufficient condition for a design to be balanced is that the matrix C of the adjusted intra block normal equation shall have all its off diagonal elements equal and all its diagonal elements equal. This will serve as a major test of balance in this work. Also a necessary condition is for the rank of C =t-1 because if the rank of C=(t-s), where s>1, then a set of [s-1} independent contrast are not estimable, but if the rank of
C=t-1; then every contrast is estimated hence the design will be connected. The paper concentrates on the quadruplicate balanced incomplete block designs.
Keywords: Balanced incomplete block design (BIBD), variance-balanced block design (VBBD), treatments, C-matrix, connected design.


(Global Journal of Mathematical Sciences: 2002 1 (1&2): 35-44)