Generating row–column field experimental designs with good neighbour balance and even distribution of treatment replications

Abstract

Blocking is a standard strategy for improving the precision of randomized experimental designs. In field trials, it is usually beneficial to impose blocks in both row and column directions. A common problem with classical randomized row–column designs is that replications of a treatment may be clustered and that some pairs of treatments appear next to each other rather more often than others. Such patterns adversely affect certain design properties which we refer to as neighbour balance (NB) and evenness of distribution (ED), and they may be particularly harmful if some of the treatments are very susceptible to environmental stresses. Here, we consider an experimental design strategy for blocked experiments that achieves good NB&ED properties. The approach is exemplified using five examples, spanning non-resolvable and resolvable replicated designs as well as partially replicated designs.