Feb.4.i9i8 Variability of Yields of Fruit Trees and Field Trials 249 



curv^e through them, and then to compare the results of the experimental 

 plots with readings taken at corresponding points of this curve. 



Wood {191 1) showed how the degree of reliance can be determined for 

 any set of experimental results by the use of the probable error. The 

 use of this constant was demonstrated in interpreting laboratory analy- 

 ses, as well as both plot and feeding experiments. Working with mangel 

 yields, the author calculates the number and size of plots required to at- 

 tain any desired precision, and working with the probabl eerror of live- 

 weight increase of sheep, tables are given showing the number of animals 

 required in an experiment to attain various degrees of reliability. 



Several papers by Harris {1912, 1913a, 19131), and 1915) have drawn 

 our attention to several phases of the experimental error in field tests. 

 A measure of the variability of the soil productivity is obtained by 

 determining the correlation between the yields of ultimate small plots 

 and the yields of various groups of adjacent plots. The more nearly 

 this correlation approaches zero, the more homogeneous the soil. This 

 method of measurement does not seem to provide as definite a means 

 of obtaining a corrective term as the use of the coefficient of variability 

 and the probable error as used by Wood, Wood and Stratton, Mercer 

 and Hall, etc., or the contingency method of correction as used by 

 Surface and Pearl (1916). 



Montgomery (1912) has also discussed the comparative variabiHty 

 resulting from increasing the size of the plot and from distributing small 

 ultimate plots over the area. The latter method was found to be more 

 accurate. In a subsequent paper {1913) the relative reliabihty of yields 

 of wheat planted in rows and in square blocks is discussed. 



An exhaustive and discriminating discussion of the nature and magni- 

 tude of variability in the results of feeding experiments has been given 

 by Mitchell and Grindley {191 3). Much of their discussion is equally 

 applicable to experimentation with plants. 



Olmstead (19 14) applied the method of least squares in calculating 

 the reliability of the yields of the mangel and wheat crop records of 

 Mercer and Hall, the potato records of Lyon, and the wheat yields of 

 Montgomery. The conclusions from this series of observations are: 



The estimation of the probable error of a large number of small duplicate plots well 

 distributed in the area devoted to a field experiment indicates that the precision of 

 agricultural experiments can be increased by replicating the experiments on small 

 plats. 



Coombs and Grantham (1916) have studied the variation in the 

 yields of rice and coconuts for one year, and discussed the range and 

 interpretation of the probable error. They showed that the yields from 

 any two single plots could only be significant when the difference 

 amounted to 22.8 per cent of the mean. They also introduced calcula- 

 tions to show the odds that any increase is a real increase and not a 

 probable error. 



