Tri.Hierarchical.IBDs

Abstract

Tri-hierarchical incomplete block design is defined as an arrangement of v treatments each replicated r times in a three system of blocks if, each block of the first system contains m1 blocks of second system and each block of the second system contains m2 blocks of the third system. Ignoring the first and second system of blocks, it leaves an incomplete block design with b3 blocks of size k3i units; ignoring first and third system of blocks, it leaves an incomplete block design with b2 blocks each of size k2i units and ignoring the second and third system of blocks, it leaves an incomplete block design with b1 blocks each of size k1 units. For dealing with experimental circumstances where there are three nested sources of variation, a tri-hierarchical incomplete block design can be adopted. Tri - hierarchical incomplete block designs can find application potential in obtaining mating-environmental designs for breeding trials. This package includes series1(), series2(), series3() and series4() functions. This package generates tri-hierarchical designs with six component designs under certain parameter restrictions.