Partially balanced bipartite block designs

Abstract

This article provides some new construction methods of partially balanced bipartite block (PBBB) designs for comparing test treatments with more than one control. Partially balanced incomplete block (PBIB) designs based on some association schemes such as triangular association, Latin-square association, group divisible association, and cyclic association are used for developing these methods of construction. A catalog of efficient PBBB designs is included for parameter values $v_1$ (number of test treatments) $\le 10, v_2$ (number of control treatments) $=2,b$ (number of blocks) $\le 8,r_1$ (replications of test treatments) $\le 10$ and k (block size) $\le 6$ along with computed variances.

KEYWORDS:

• Group divisible association
• group divisible partially balanced bipartite design
• partially balanced incomplete block design
• partially balanced bipartite block design
• triangular association

Acknowledgments

The first author is grateful to PG School, ICAR-IARI, New Delhi, and ICAR-IASRI, New Delhi for providing the requisite facilities to carry out this investigation. The authors thank the Editor-in-Chief and anonymous reviewers for their valuable suggestions and helpful comments which led to considerable improvement in the article.

Disclosure statement

There is no potential conflict of interest.