52 



BREEDING CROP PLANTS 



certain contiguous units tend to yield high while others show a 

 tendency in the opposite direction. Under these conditions a 

 high correlation coefficient results. If variability due to random 

 sampling only is entering, the correspondence between some 

 contiguous plots will be counterbalanced by the lack of corre- 

 spondence between others, providing that the number of ultimate 

 units is sufficiently large to permit an expression of the law of 

 average. It is obvious that in the application of Harris' method 

 the field must receive the same treatment (seed, cultivation, 

 fertilizer, etc.). The division of the field into the desired units 

 may be made at any time before the crop is harvested, but 

 preferably before or soon after planting in order to minimize 

 possible injury to the growing crop. 



A simple illustration will make the calculation of the correla- 

 tion coefficient clear, although a much larger number of units 

 should be used in an actual study of the reliability of a field for 

 plot work. Suppose a certain field is divided into 16 units and 

 these units are in turn arranged in groups. Let p\, p2, Pz, etc., 

 represent the ultimate units and C Pl , C PV etc., represent the 

 groups. By assigning values for yield in bushels per acre to the 

 ultimate units, one may make the calculation necessary to apply 

 the formula. The value of any particular group is the sum of 

 the ultimate units in it. 



DIAGRAM ILLUSTRATING HARRIS' METHOD 



p = Average yield of all ultimate units = 

 n = Number of units in each group = 

 n = Number of groups = 



= Sum of squares of the yields assigned 

 for ultimate units = 



4 

 4 

 4 



280 



S(C P 2 ) = Sum of squares of the group yields = 1,080 

 <T P = Standard deviation of assigned yield 



for the ultimate units = vT5 = 1.2247 



<V> = (1.2247) 2 = 1.4999 



The numbers enclosed in parentheses represent assumed values (bushels 

 per acre). 



Now according to the formula 



