Random generation and selection of one- and two-dimensional designs for experiments on blocks of natural size

Abstract

Many incomplete block design strategies have been devised to improve the efficiency of experiments. However, the constraints imposed by these designs can be unrealistic because natural blocks may not be all the same size or there may be no conventional designs for required treatment, replication, block and plot combinations. In addition, because of similar constraints, two-dimensional block designs—the so called row-column designs— are used less frequently than the occurrence of conditions where their use would result in greater experimental efficiency. This article explores the properties of an easy to use random generation and selection strategy for obtaining block and row-column designs. Although the strategy does not necessarily obtain the best possible designs when judged by any one of the many criteria, this apparent disad vantage is outweighed by the generality and ease of use. It is concluded that present-day model fitting methods remove the constraints which have been traditionally imposed on designs and the benefits of using block designs can be extended by the use of informal design methods.