Multivariate Analysis and Agricultural Experiments

Abstract

The aim of statistical science must always be to aid the research worker in making the best possible use of his efforts and his results; one important function for Biometrics is to provide a forum for the exchange of opinions on how this aim can be achieved in the biological sciences. Amongst the many papers on statistical science published today, some appear to find new outlets for mathematical theory without materially assisting scientific research. In recent years, I have been particularly aware of papers of this kind on multivariate analysis. Statisticians evidently hold widely divergent views on the practical importance of various types of multivariate analysis: I suggest that we need to examine carefully their relevance to the interpretation of experimental and observational data. In this note, I propose to be severely critical of the use of multivariate analysis of variance and the construction of canonical variates in the analysis and interpretation of agricultural and other experiments. My argument can best be presented by reference to a particular example, and I therefore discuss in detail the recent paper by R. G. D. Steel (1955). Of course I intend no personal attack on Dr. Steel's work, but his interesting paper happens to illustrate my criticisms especially simply and clearly. Employment of the methods he describes appears to be increasing, and other applications that are, in my view, equally unfortunate can be found (e.g., Dutton, 1954; Quenouille, 1950). Questions of choice of method are often less simple than an ardent partisan would have them: I look forward to having my own outlook criticized as severely as I criticize that of Dr. Steel and others, for clear thinking about the ultimate objectives of statistical analysis is more important than the vindication of a particular point of view. Steel has discussed an experiment comparilng the yields of 25 varieties of alfalfa, grown on the same four randomized blocks in 1949 and 1950.