Optimal row-column designs for CDC method (1)

Article type: Research Article

Authors: Sharma, Mahendra Kumar^* | Tadess, Mekonnen | Ibrahim, Mohammed Omer

Affiliations: Department of Statistics, Addis Ababa University, Addis Ababa, Ethiopia

Correspondence: [*] Corresponding author: Mahendra Kumar Sharma, Department of Statistics, Addis Ababa University, Addis Ababa, Ethiopia. E-mail: [email protected].

Abstract: In the present article, we are presenting row-column designs for Griffing’s complete diallel cross methods (1) for p parents by using a complete set of (p-1) mutually orthogonal Latin squares, when p is prime or a power of prime. The row-column designs for Griffing’s methods (1) are new and universally optimal in the sense of Kempthrone (1956) and Kiefer (1975). The row-column designs for methods (1) are orthogonally blocked designs. In an orthogonally blocked design no loss of efficiency on the comparisons of interest is incurred due to blocking. The analysis includes the analysis of variance (ANOVA), estimation of general combining ability (gca), specific combining ability (sca) and reciprocal combining ability (rca). Tables of universally optimal row-column designs have been provided.

Keywords: Mutually orthogonal Latin squares (MOLS), complete diallel cross (CDC), row-column design, optimality

DOI: 10.3233/MAS-211307

Journal: Model Assisted Statistics and Applications, vol. 17, no. 3, pp. 155-159, 2022