Tetrahedral and cubical association schemes with related PBIB(3) designs

Article type: Research Article

Authors: Sharma, V.K. | Varghese, Cini^{; *} | Jaggi, Seema

Affiliations: Indian Agricultural Statistics Research Institute, Library Avenue, New Delhi -110 012, India

Correspondence: [*] Corresponding author. Tel.: +91 011 25836230; Fax: +91 011 25841564; E-mail: [email protected].

Abstract: Here, two three-class association schemes called tetrahedral association scheme and cubical association scheme have been proposed along with methods of constructing partially balanced incomplete block designs based on these schemes. Designs based on cubical association scheme are found to be resolvable. An outline of the method of analysis of the designs has also been presented together with a list of PBIB(3) designs obtained using the proposed methods for number of treatments v < 100. The proposed designs are seen to be more efficient than the circular lattices [PBIB(3) designs] with the same number of experimental units for the estimation of elementary treatment effect contrasts.

Keywords: Partially balanced incomplete block designs, tetrahedral association scheme, cubical association scheme

DOI: 10.3233/MAS-2010-0146

Journal: Model Assisted Statistics and Applications, vol. 5, no. 2, pp. 93-99, 2010