Optimal block designs for CDC experiments method (2)

Abstract

Incomplete block designs for a complete diallel cross (CDC) experiment known as method (2) of Griffing (1956) are proposed. These designs are derived by using mutually orthogonal Latin squares of order p, when p is a prime integer or power of a prime integer. With p inbred lines, the [p(p + 1)/2 − 1] degrees of freedom, for this method of Griffing, are partitioned into two orthogonal sets of (p − 1) and p(p − 1)/2 degrees of freedom the former for general combining ability (g c a) and the latter for specific combining ability (s c a) effects, respectively. These designs are optimal in the sense of Kempthorne (1956). The analysis includes the analysis of variance and the estimation of general combining ability and of specific combining ability. The analysis is illustrated numerically.