Computer assisted design of experiments

It is now generally true that the computer is widely used for analysing data from comparative experiments but relatively little attention has been paid to how the computer can assist at the design stage of an experiment. This thesis attempts to remedy this situation. In Chapter 1 an attempt is made to formalize the conversation that takes place between an experimenter and a statistical consultant with a view to transferring the consultant's skills to the computer. To determine the difficulties involved experiments to compare two treatment means are considered. Where there are more than two treatments it is essential to determine which treatment comparisons are important. Existing computerised algorithms for constructing suitable experimental designs deal solely with the case where there is an equal interest in all treatment comparisons and where all blocks are of the same size. Chapter 2 describes an algorithm without these limitations. It searches for treatment interchanges that improve a given design. In Chapter 3 this algorithm is extended to cover row- and-column designs. A further algorithm is required to combine component designs. One disadvantage of these algorithms is the invariance of the treatment replications once chosen. In Chapter 4 completely different algorithms without this disadvantage are developed. They are based on an exchange procedure and an interchange procedure.