410 SECTIONAL TRANSACTIONS.— M. 



Discussion on Plot Technique. Dr. R. A. Fisher ; Mr. T. Eden ; 

 Dr. E. S. Beaven ; Mr. A. Millar. 



Dr. R. A. Fisher. — The development of modern methods of plot arrangement is 

 intimately connected with the development of an exact statistical technique for 

 examining the results obtained. This goes back to ' Student's ' paper of 1908. A 

 compact arithmetical procedure is now in use, called the Analysis of Variance, which 

 embodies the exact treatment developed from ' Student's ' method. The essence of 

 this method of analysis lies in dividing the total amount of variation observed between 

 the plot yields into separate portions, some representing experimental effects to be 

 utilised, others, perhaps, experimental effects to be eliminated, while at least one 

 portion represents the experimental errors to which the results are liable. To each 

 portion is assigned a definite number representing the degrees of freedom, and these 

 numbers depend on the structure of the experimental design ; the analysis into 

 degrees of freedom is useful, not only in guiding the arithmetical procedure in the 

 analysis of the results, but in determining to what questions a given experiment 

 could give definite answers, and how many independent comparisons would be 

 available to answer each such question. 



The first step towards the development of a sound field technique was taken in 

 the uniformity trials, such as those of Wood and Stratton and of Mercer and Hall in 

 1910. These showed unmistakably that by far the greater part of the errors of field 

 experimentation were due to soil heterogeneity, and only much smaller errors were 

 introduced in the measurement of the land, the separation and weighing of produce, 

 &c. The errors due to soil heterogeneity can be reduced by (1) replication, or assigning 

 to each treatment or variety a number of plots, and (2) the elimination of certain 

 components of the soil heterogeneity which, as the uniformity trials also show, is 

 best done by eliminating the differences in fertility between whole areas, rows, columns 

 or blocks containing a number of adjacent plots. When such elimination is effected 

 in the field it is essential that it shall also be done in the statistical procedure by which 

 the experimental error is estimated ; equally it is important that the portion of the 

 soil heterogeneity which is not eliminated shall be deliberately randomised, in order 

 that the estimated error shall correspond to the real errors affecting the results. 

 Personal judgment of a fair distribution of plots is not a satisfactory substitute for 

 actual randomisation. Slides were exhibited illustrating the lessons of uniformity 

 trials, and some of the field arrangements adopted this year at Rothamsted based 

 upon these principles of experimental design. 



Dr. E. S. Beaven said that he had been conducting replicated experiments with 

 cereals for the last twenty years, but only for comparisons of yield of different varieties, 

 and he would refer only to such trials. Seven years ago he designed the half -drill 

 strip method for field experiments (Jrl. Min. Agr., Nos. 4 and 5, 1922), and this had 

 been adopted by the National Institute of Agricultural Botany at their stations in 

 various parts of England for the past five years. Replication was the first essential, 

 and the question whether the arrangement of the plots should be systematic or 

 ' randomised ' was of comparatively minor moment. A diagram which was exhibited 

 showed that the same number of replications could be obtained on the same area in 

 the case of yield trials of varieties by this method as by Dr. Fisher's method, and it 

 might be strongly contended that the small increase of accuracy, if any, obtained 

 by the ' Latin Square ' method was of much less moment than its practicability under 

 field conditions. The ' Latin Square ' method was impossible, or at least extremely 

 difficult, of execution in trials of varieties with the customary implements of 

 husbandry. In an agricultural section it was hardly necessary to say that it was not 

 possible to lift and transport drills and reaping machines from plot to plot by 

 aeroplanes. It was necessary to use horses or tractors — which could be done easily 

 in the half -drill-strip system — but would present extraordinary difficulties in field 

 plots laid out on the ' Latin Square ' system. It was very necessary in the design 

 of such trials not only to know the mathematical theory of probability applicable to 

 such experiments, but also to have a knowledge of the material under investigation, 

 and of agricultural practice. 



A previous application of Dr. Fisher's theories of ' analysis of variance ' and 

 ' degrees of freedom ' to an experiment in 1923 on ' Manurial response of different 

 varieties of Potatoes ' led to the conclusion that ' there is no significant variation in 

 the response of different varieties to manure.' This appeared to be contrary to 

 common sense. It was a well-established general proposition that races of the same 



