Economic Choice of the Amount of Experimentation

Summary When a new process is suggested for use in agriculture or technology it is usually necessary to carry out experiments to estimate the increase in output that would result if the new process replaced that in current use. If the cost of experimentation and the scale of potential application of the new process are known, one method of arriving at an optimum amount of experimentation is to minimize the total risk given by the sum of the cost of the experiment plus the expected loss due to wrong decisions. The main difficulty is that the last quantity depends on the true increase in output due to introducing the new treatment, which can only be estimated from the results of the experiments. The paper discusses the case where an initial experiment is carried out, and it is required to decide whether to accept or reject the new treatment at once or else to carry out further experimentation. In the latter case the optimum amount of further experimentation has also to be decided. A solution is provided by minimizing the risk after eliminating the unknown parameter by averaging over its fiducial distribution based on the evidence from the initial experiment. Means for applying the resulting decision rule in practice are provided, and its performance under various circumstances is discussed.