XIII.] CALCULATION OF EXPERIMENTAL ERROR 363 



collected into ten groups of five years each, we should 

 get the following figures for Plot 12 — 105, 121, 128, 121, 

 108, 102, 96, 114, 123, 121. In all cases except one the 

 five years' average of Plot 12 is higher than that of Plot 

 3, and as we can calculate as before that the mean error 

 attached to each figure is ± 10-5, we could hardly have 

 concluded with confidence from any five years' series that 

 Plot 12 was superior to Plot 3, and the extent of the 

 superiority would have remained unknown. 



To take another example, Table CIV. represents the 

 results of five years' experiments with different crops on 

 five similarly treated plots in Little Hoos field, reduced 

 each year to a common standard by taking the mean of 

 the five as 100. 



Table CIV. 



Again, it will be seen that the variations from the 

 mean of the single plots in any given year are consider- 

 able, the mean error being ± 7-5, on the assumption that 

 all the plots should be exactly alike. But from the five- 

 year means there would seem to be some constant 

 difference in the plots, which improve from A to D, 

 though the superiority indicated is still of much the 

 same magnitude as the experimental error, and that can 

 only be reduced by continuing the trials over a longer 

 series of years. 



It will not be necessary to go into further detail, but 

 the above numbers illustrate the general principle that 



