SOME SYSTEMATIC EXPERIMENTAL DESIGNS

Consider the following experiment. It is required to compare the effect in processing of a number of treatments applied to wool. The wool is divided into lots as alike as possible and the lots are numbered in random order. In week 1 lot 1 is processed with a certain treatment. In week 2 lot 2 is processed with, in general, a different treatment. And so on. The age of the wool affects its behaviour in processing so that, superimposed on any treatment differences, there will be a smooth trend due to aging. We want to estimate the treatment differences as simply and accurately as possible. In what order should the treatments be applied? More generally, consider an experiment to compare a number of treatments on plots arranged in order in space or time, one treatment being applied to each plot. We assume that the measured quantity is (Treatment constant) + (Smooth trend) + (Random quantity), (1) where the random quantity has zero mean, constant variance and is independent in different plots. We want to arrange the treatments to give simple and accurate estimates of the treatment differences. One method is to arrange the experiment in randomized blocks, thus eliminating part of the trend from the error of the treatment comparisons. A second method is to randomize completely the order of application of the treatments and to eliminate the trend by analysis of covariance on position. The calculations can be extensive if high-order trends are involved. Also when the above assumptions hold information is lost by the use of the method. The loss may be serious if the number of treatments and number of replicates are small (see ? 4 2).