Nonresolvable Row–Column Designs with an Even Distribution of Treatment Replications

When generating experimental designs for field trials laid out on a rectangular grid of plots, it is useful to allow for blocking in both rows and columns. When the design is nonresolvable, randomized classical row–column designs may occasionally involve clustered placement of several replications of a treatment. In our experience, this feature prevents the more frequent use of these useful designs in practice. Practitioners often prefer a more even distribution of treatment replications. In this paper we illustrate how spatial variance–covariance structures can be used to achieve a more even distribution of treatment replications across the field and how such designs compare with classical row–column designs in terms of efficiency factors. We consider both equally and unequally replicated designs, including partially replicated designs. Supplementary materials accompanying this paper appear online.