On the construction of trend free constant block sum PBIB designs

Abstract

Agricultural and industrial experimentation may often witness the effect of systematic trend. Trend effects, though remote, may still influence the response under consideration. The incorporation of trend effects in the model thus paves the way for proper model specification. Completely trend robust block designs, which are commonly known as trend-free block designs, are an important class of block designs in such a way that the analysis can be done in the usual manner as it could be done in case of normal block designs due to orthogonal nature of trend effects and treatment effects. This article deals with the construction of some classes of completely trend robust i.e. trend free constant block sum partially balanced incomplete block (TFCBS-PBIB) designs along with characterization properties. SAS macros have also been developed and made available in public domain to provide readymade solutions to the end-users.

Keywords:

• Association scheme
• Constant block sum
• Information matrix
• Partially balanced incomplete block designs
• SAS macros
• Trend

AMS SUBJECT CLASSIFICATION:

• 62Kxx
• 62K10

Acknowledgments

First author duly acknowledges Indian Council of Agricultural Research for providing junior research fellowship during his M.Sc period. First author also acknowledges Graduate School, ICAR-Indian Agricultural Research Institute, New Delhi for all kind of support they have provided during his M.Sc. tenure.

Disclosure statement

The authors have declared no conflicts of interest for this article.

Additional information

Funding

This study was supported by the ICAR JRF Fellowship.