The Analysis of Experiments on Growth Rate

comparable groups of growing subjects over a period of time. The attribute of interest to the experimenter-e.g., liveweight-is measured initially and at regular intervals during the experimental period. The results of such an experiment are most commonly considered in terms of average growth rate-e.g., gain in liveweight per week-and this quantity is most simply obtained by dividing the difference of the initial and final measurements by the duration of the experiment. Experiments of this type were discussed by Wishart 1938, 1939. He pointed out that this method of assessing growth rate ignored any information provided by the intermediate measurements, and that other features of the growth curve besides the average slope might merit consideration. Difficulties arise, however, because successive measurements on the same subject cannot be considered independent. Wishart accordingly suggested that the growth curve for each subject should be broken down into its mean and linear, quadratic, etc., components, each of these being subjected to separate analysis. The effects of treatments on the average growth rate could be seen from the analysis of the linear components, and analyses of the further components would show to what extent the treatments were affecting the shapes of the growth curves. In an experiment of short duration, or when the treatment effects are small, a summary solely in terms of average growth rate will often be adequate. When a single treatment is compared with a control, this is equivalent to assuming that the treatment effect-the average difference between treated and control subjects-increases linearly with time. It is natural to estimate this effect from the difference between the linear components of the growth curves. However, in many types of