588 TRANSACTIONS OF SUB-SECTION B. 



(iii) The Accuracy of Feeding Experiments. 

 By Professor T. B. Wood, M.A., and A. B. Bruce. 



In the published results of feeding experiments on the comparative merits of 

 different diets for cattle and sheep there is a tendency to base conclusions on the 

 average result of a single experiment with a small number of animals without 

 regard to the degree of variability between different individuals. 



If no regard be paid to individual variability it is desirable either to experi- 

 ment with a larger number of animals in each lot than has hitherto been customary, 

 or to repeat the experiment several times. 



In the case of cattle a very usual number is six, and eight is practically the 

 maximum. A consideration of the published figures for individual animals 

 justifies the assertion that these numbers are so small that the average has very 

 little weight. In fact, the individual variations are generally so large that it is 

 doubtful whether trustworthy results can be obtained with fewer than twenty 

 animals. 



A measure of the reliability of the mean result of an experiment can be 

 obtained by calculating the probable error from the individual results. This is a 

 measure of the variability, inasmuch as the figure gives the limits within which 

 it is an even chance that the mean will lie. From a consideration of the figures 

 obtained in a feeding experiment carried out under the supervision of the 

 Cambridge School it is shown how fallacious any conclusions based on the mean 

 of a small number of animals may be. 



From a general review of feeding experiments it is suggested that an investiga- 

 tion of the causes (and perhaps the heredity) of individual variations in the 

 capacity for fattening might be likely to lead to practical and useful results. 



In arranging feeding experiments the common practice is to endeavour to select 

 animals of equal weight and age and to make preliminary tests so as to pick out 

 those of uniform fattening capacity. It is suggested that in order to ensure that 

 the results of different experimenters should be comparable, either a uniform 

 conventional method of selection should be adopted or selection should be avoided. 



(iv) The Sampling of Agricultural Products for Analysis. 

 By Professor T. B. Wood, M.A.. and A. B. Bruce. 



The discrepancy between the analyses of agricultural products published by 

 different chemists may be due to divergent methods of taking samples. It is 

 accordingly desirable to give some consideration to the law of error in this 

 connection. 



To illustrate and explain the application of this law to sampling, certain 

 figures obtained in an investigation into the composition of mangels are given. 

 The most important formula in this connection is that which states that the 

 accuracy of the analysis of a sample taken from a number of individuals is 

 proportional to the square root of the number of individuals comprised in the 

 sample. Thus, if a certain sample gives a probable error of r, and it is desired to 

 obtain a figure for the mean with a probable error of -gr, the sample should consist 

 of four times as many individuals. The mangel results referred to above are 

 used to prove the accuracy of this statement. 



(v) The Error of Experiment in Agricultural Field Trials. 

 By A. D. Hall, F.B.S., and E. J. Russell, D.Sc 



Analysis of the causes of error show that they fall under several heads : — 



(a) Lack of uniformity in the toil. — Even on a level field where no obvious 

 variation occurs analysis shows that there are certain differences in different 

 parts of the field. A sensitive and at the same time simple test is to ascertain 

 the percentage of moisture in samples of soil collected to the same depth — six or 

 nine inches — and as nearly as can be at the same time. The differences commonly 

 amount to five (or in dry fields to ten) per cent, of the moisture present. Another 

 factor greatly influenced by variations in the soil is the amount of nitrate present. 



