A Comparison of Super-Valid Restricted and Row–Column Randomization

Abstract

In complete block experiments, treatments are often randomized within blocks without any other restrictions. When the blocks are rows of plots and the blocks are laid out in parallel so that also columns of plots are formed, there might be random effects of both rows and columns. In this situation, a row–column design is a natural choice. Super-valid restricted randomization is another option. This article compares these randomization procedures for small complete block experiments (5–10 treatments in 3–6 blocks). Validity of a randomization procedure is defined for mixed-effects models. The two randomization procedures are compared with regard to average variance in pairwise comparisons. Row–column randomization is recommended when either there are at least four replicates, or the number of replicates is three and intercolumn variance is not known to be small. These conclusions assume a model with fixed effects of treatments and random effects of rows and columns, and estimation using the REML method and the Kenward and Roger approximation.