Partially balanced nested block designs based on 2-associate-class association schemes for test-control comparisons

Abstract

In this article, nested partially balanced treatment incomplete block (NPBTIB) designs are introduced for making test treatments-control treatment comparisons. Several methods of constructing such designs are presented. These methods of constructions utilize group divisible treatment (GDTD) designs, nested balanced incomplete block (NBIB) designs, and nested partially balanced incomplete block (NPBIB) designs. A catalogue of efficient NPBTIB designs with 2-associate classes for the number of treatments $v\le 16,$ replications of test treatments $r\le 15,$ and replications of control treatment $r_0\le 30$ is also included.

Keywords:

• A-efficiency
• Group divisible treatment design
• Nested balanced incomplete block design
• Nested partially balanced incomplete block design
• Nested partially balanced treatment incomplete block design

Acknowledgments

The authors express our gratitude to the editor-in-chief and the anonymous referee for their invaluable suggestions and constructive comments, which have significantly contributed to enhancing this manuscript.

Disclosure statement

On behalf of all authors, the corresponding author states that there are no conflicts of interest.