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



can expect, supposing all the conditions to have been favour- 

 able. Of course, after a set of field plots have been laid out, 

 great variations in the soil may reveal themselves, due either 

 to changing subsoil and drainage or to some past irregularity 

 of manuring or cropping. Again, the plots may suffer most 

 irregularly from some insect or fungoid attack. In these 

 cases one must ignore the results entirely, and begin afresh. 

 But supposing the field to be sensibly uniform and a good 

 stand to have been obtained, what sort of differences in the 

 yields from two plots may be taken to indicate an effect of 

 the treatment they have received, and what must be regarded 

 as covered by the natural variation due to unknown causes ? 



We may take the Rothamsted experiments as satisfying all 

 the external conditions of accuracy ; the land is reasonably 

 uniform, more care is given to the plots than would be 

 possible under ordinary farming conditions, while the staff 

 have both experience and organisation to ensure accuracy 

 in weighing and measuring the produce. If we then select 

 from the Rothamsted records various pairs of plots receiving 

 the same treatment, we find at once that they do not give 

 similar yields year by year, but vary with considerable irregu- 

 larity. As an example, we may take the two unmanured plots 

 on the grass field and set down both their actual and relative 

 yields for the last fifty years. If the soil of the two plots is 

 identical, they should show the same result after a certain 

 number of years; but if there is some permanent difference 

 between the two revealed by the averages, it will be possible 

 to see how far this difference would be made evident by a 

 single year's trial. 



Looking at the relative yields set out in Table I., we see 

 that Plot 12 in 37 years out of the 50 gave a bigger crop than 

 Plot 3, but on 13 occasions it gave less : taking the mean of 

 the whole period, its relative yield is no against 100 for 

 Plot 3. Granting, however, that it is really about 10 per cent, 

 the better plot, there have been many years when it gave a 

 30 per cent, better yield, and in one year it was 96 per cent, 

 better; on the other hand, it was on two occasions 10 per 

 cent, below Plot 3. Mathematicians have devised a process 

 whereby we can calculate from such a collection of results the 

 value we may safely attach to the result, and using this 



