Restricted randomization for neighbour-balanced designs

In experiments with a spatial layout, there may be problems if neighbouring treatments are likely to interfere with each other. Combinatorics can often provide designs with a reasonable amount of "neighbour balance": however, the usual full randomization process destroys such balance. Restricted randomization can preserve the balance, but may impose a more complicated analysis of variance than that originally envisaged, which in turn has further implications for the design problem. In practical cases the numbers involved do not always lead to tidy solutions, and one may have to choose between doing a technically correct, but complicated, analysis of variance (with the attendant difficulties of interpretation to the client) and making simplifying assumptions or approximations that permit a straightforward analysis to be done.