On the construction of trend resistant PBIB designs

Abstract

In agricultural, animal, fisheries and industrial experimentation under block design setup, systematic trend may affect the response under consideration. Although remote, these effects may still have high influence on response and hence should be incorporated in the model for proper model specification. Completely trend resistant block designs, also known as trend free block designs, are an important class of designs where the analysis can be done in usual manner as in case of normal block designs since trend effects and treatment effects are orthogonal. Literature is available on different aspects of trend resistant incomplete block designs mainly focusing on balanced incomplete block designs. This article deals with the construction of completely trend resistant Partially Balanced Incomplete Block (TR-PBIB) designs. Two methods of constructing such designs have been discussed. The information matrices for the class of designs developed have been derived and SAS code for the generation of the developed designs has also been provided.

Keywords:

• Association scheme
• Information matrix
• Partially balanced incomplete block designs
• SAS code
• Trend

MATHEMATICS SUBJECT CLASSIFICATION:

• 62Kxx; 62K10; 05B05

Acknowledgements

We are thankful to the editor and referee for their constructive suggestions which have helped in improving the quality of the manuscript. Second author is thankful to Indian Council of Agricultural Research for providing Junior Research Fellowship during his M.Sc. (Agricultural Statistics) tenure. We also acknowledge the facilities provided by ICAR-IASRI, New Delhi, P.G. School, IARI, New Delhi, ICAR-CMFRI, Kochi, for conducting the research.