Feb. 4, 1918 Variability of Yields of Fruit Trees and Field Trials 265 



per cent of the mean production. That is, the chances are even that any 

 plot as described, of 32 trees, will fall within ±10.02 per cent above or 

 below the true mean. The chances are equally as good that such a plot 

 will not fall within the accuracy of ± 10.02 per cent of the mean. In 

 comparing two such plots, both with the same probable error of ± 10.02 

 per cent, the probable error of such a comparison will be greater than 

 the probable error of one — that is, it will be equal to ±10.02 per cent 

 xV2=± 14-17 per cent. Therefore, if plots undergoing differential 

 treatment vary from each other by only ±14.17 per cent of the mean 

 of the plantation, half the time such differences in yield may be due to 

 the treatment, and half the time they may be due to casual variation. 



It is clear, then, if fertihzer or irrigation experiments laid out in such 

 plots differ from each other by only 14.17 per cent of the mean produc- 

 tion of the total area, we are not assured beyond an even chance that the 

 difference is a real difference due to the factors which are being experi- 

 mented upon. So slight an assurance can hardly be expected to be 

 sufficiently reliable to prompt a farmer to purchase fertilizer, to change 

 his method of irrigation, or to undertake any new business; much less 

 will this assurance justify an experimenter in drawing conclusions from 

 the result of a field trial. 



Our present knowledge of orchard fertilization in the arid West will 

 hardly justify any assumption on our part more reliable than an even 

 chance that one fertilizer will produce an increased yield of fruit com- 

 pared with another, or even cause an increase over an untreated plot. 

 The same thing may be said in comparing different methods of irrigation. 

 In most cultural trials we would therefore be comparing two results 

 where the difference may occur in either direction. (Tables V and VI. )^ 



Table V. — Table of odds for differences which may occur in cither direction 



' Tables V and VI are taken from the writings of Wood (igii) who in turn adopted thexn "from one of 

 the standard reference books on astronomy. " 



