Experimental Designs

This is a revision of a book which has already become established as an authoritative text on the design of experiments. It gives both an exposition of the practical aspects of this subject, as interpreted in modern statistics, and also a brief account of the mathematical model underlying each design. It is assumed that the reader has previously had an introduction to statistical methods, particularly the analysis of variance, though there is an excellent but compact review of the analysis of variance and covariance in Chapter 3. There are many aspects of the design of experiments other than the statistical aspects. The scientist who first defines the problem is usually the one who makes the most important contribution to the design of the experiment , and this is particularly so when the experiment is concerned with theoretical issues rather than simple applications. At other times, the elaboration of a piece of apparatus, or of a technical method, may be the critical contribution to the solution of a problem. In neither of these two cases are statistical considerations usually of any importance, or, indeed, of any relevance. The experimenter who thinks of reading this, or any other statistical book on experimental design, should be warned that many things of importance to him in the design of his, experiments are not within the scope of such books. The statistical treatment of experimental design is concerned, for the most part, with the method of selecting the sample from the population of interest. Nothing that has been written above is intended to minimize the importance of this step. If due care is not taken, two types of error may be made. The least serious of these is that efficiency may be reduced, in the sense that 100 observations may be used to provide information that could have been obtained equally well from 20. This loss of efficiency may cost time and money, and, in certain cases where there are various limitations on the amount of material available, an experiment may not even be undertaken, because the experimenter is unaware of the possibility of devising a design of adequate efficiency. The second type of error that may arise from neglect of statistical design is more important. An experiment may be set up in such a way that valid conclusions are impossible. A classical example is the Lanarkshire Milk Experiment, conducted many years ago to find …