368 The Experimental Error in Field Trials, [aug., 



which have received exactly the same treatment ; in order to 

 make it easier to judge the figures, the actual yields each year 

 have been reduced to a common standard, taking the mean of 

 all the five plots as 100. 



The experiment had to be started on the assumption that 

 all the plots were exactly alike, and if so, the mean error 

 attaching to the result of a single plot in any year is 7*5 per 

 cent., but with the five years' trials it is beginning to be clear 

 that there are some real permanent differences between the 

 plots, which improve from A. to E. Still, whatever may be 

 the real position of each plot as revealed after further years of 

 experiment, we may expect in any one year to find a parti- 

 cular plot 7*5 per cent, in error on one side or the other. 



Space does not permit of the consideration of more cases, 

 but the general result of the examination of many series of 

 experiments indicates that the mean error attached to the 

 yield of a single plot is about 10 per cent, plus or minus. In 

 other words, if we have three experimental plots giving yields 

 of 91, 100, and 109 respectively in any one year — for example, 

 18, 20, and 22 tons of roots — it is not right to conclude that 

 such differences have been brought about by the treatment; 

 the three plots must be considered as giving equal results. 

 Of course this figure is obtained from a consideration of the 

 Rothamsted results only, and other soils might be found on 

 which the conditions were so much more uniform that the 

 experimental error would be reduced and a closer agreement 

 between duplicates would prevail. The examination I have 

 made of other data, however, though they do not permit of 

 working out the mean error over such long periods, yet lead 

 me to suppose that a 10 per cent, error is near the truth gener- 

 ally, and may be taken as a safe guide for working purposes. 

 In the records of experiments a good deal of strained argu- 

 ment is often spent in explaining results or drawing conclu- 

 sions from them when the differences are much less than the 

 10 per cent, which we have thus found to be the average error 

 attaching to a result obtained under favourable conditions. 

 Much of this might have been spared if the experimenter had 

 kept clearly before him the fact that nothing less than 20 per 

 cent, differences have much significance in a single experi- 

 ment. The only way of reducing the experimental error and 



