Showing papers in "Calcutta Statistical Association Bulletin in 1967"

A New Type of Higher Associate Cyclical Association Schemes

Abstract: 1 .. Introduction. In earlier publications (Nandi and Adhikary, 1965; Adhikary, 1966) it has been shown how the concept of two associate cyclical association scheme of Bose and Shimamoto (1952) can be extended to yield such higher associate schemes. The group of treatments was there divided into subgroups and some of the subgroups were again divided into two subsets satisfying conditions similar to those of Bose and Shimamoto (1952). The purpose of this note is to show that, more generally, if the group of treatments can be divided into more than two subsets (not necessarily subgroups) satisfying certain conditions, it is possible to obtain higher associate cyclical association schemes. This generalisation includes the association schemes given earlier as particular cases when some of the subsets are subgroups. It will further be shown that the cubic designs of Raghavarao and Chandrasekhararao ( 1964) belong to this general class.

Group Divisible Designs with Variable Replications

Abstract: Group divisible designs with variable replications (introduced here) form an important subclass of 'Balanced block designs with variable replications' (Adhikary, 1965) and themselves include the group divi5ible incomplete block designs (G . D. designs) of Bose and Connor (1952) and H . G . D. designs with three associate classe, of Roy (1954, 1955, 1962). They may be defined as follows. An incomplete block design with v treatments in b blocks of k plots each is said to be a group divisible design with variable replications if the treatments can be divided into (.u1 + /L~)-gro ups satisfying the follo\\\\·ing conditions :