458 Journal of the Department of Agriculture. — Nov., 1922. 



neighbour, and it is inipossi})le to asciibe llie difference to any cause 

 tlian individual variation. 



For example, in fattening experiments conducted in South Africa 

 with a group of four old oxen selected as nearly alike as possible, 

 one animal made three and a lialf times tlie gain of another, and in 

 another experiment conducted on similar lines one animal made 

 eleven times as much gain in weight per day as another. 



These are exceptional cases, but they show the extreme variation 

 possible, and indicate how careful it is necessary to be, in drawing 

 nice conclusions from the results of single animal or single plot 

 experiments. 



FiELn Trials. 



Causes of Variation. 



The variation in the yields of plots similarly treated is due 

 partly to difference in soil and partly to the influence of numeroiLs 

 small factors, such as uneven seeding and manuring and cultivation, 

 errors in weighing, eft'ect of birds, insects, previous crops, etc., the 

 effect of which can never be accurately gauged beforehand. 



Figures obtained from Rothamsted illustrate the two kinds of 

 variation very well. xVt that station the yields of hay from two plots 

 of grass in the same field have been recorded every year since 1856. 

 The measurements and weights were recorded by skilled and experi- 

 enced officers, and the experiment has throughout been conducted as 

 thoroughly as could possibly be. Taking the figures for the whole 

 period of fifty years, the one plot is found to average 10 per cent, 

 higher than the other, a result no doubt largely due to difference in 

 soil. In individual years, however, tlie plot which averaged 10 per 

 cent, greater, was 49 per cent, greater and 10 per cent, less than that 

 of the other, this random variation being due to various factors. 



Even in five-year periods absolutely reliable results cannot be 

 obtained, and the above experiments furnish striking evidence of 

 this. As stated, one plot over the whole period averaged 10 per cent, 

 greater than the other. In five-year periods, however, the one plot 

 averaged 28 per cent, greater and 4 per cent, less than the other, 

 showing that a difference in yield between the two plots gained over 

 an average of five years could not be considered absolutely reliable. 



Farmers generally hold the belief tliat for reliable results to be 

 obtained the plots ought to be large. I'iXperiment, however, shows 

 Ihat llie difference in yield of a croj) due to difference in soil is 

 greater in large plots than in small, and that the only way to nullify 

 the effect of the variation in soil is to repeat the plots several times 

 in a systematic way. 



If it be desired in field experiment to reduce the error to a small 

 figure in the region of, say, 2 per cent., it is necessary to replicate 

 the plots five times. Thus, if one factor were under test, e.g. the 

 effect of fertilizing with a definite quantity of superphosphate, five 

 plots fertilized would need to be interspersed systematically with five 

 plots unnumured; and a convenient and suitable size for each plot 

 would be from one-fortieth to one-tenth of an acre. 



Averages. 



The opinion generally held is that an average is a reliable figure, 

 giving a true representation of the range of results under considera- 

 tion. There are many limitations, however, to the use of an average. 



