Optimal randomization for experiments in which autocorrelation is present

Abstract

For a linear or spatial ordering of the experimental units, systematic methods of applying the treatments to the experimental units minimize the variance of linear contrasts of treatment means. In the linear ordering the optimal randomization scheme for the application of k treatments is to apply a treatment to every k th experimental unit, the equivalent of systematic sampling in the sampling literature. In the spatial ordering the optimal randomization schemes are equivalent to Quenouille's (1949) systematic aligned or unaligned spatial sampling schemes.