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)
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