416 Plant-Breeding 



horizontal array would be a distribution of number of pods 

 with respect to length of plant. But if we add up all the fre- 

 quencies along each horizontal array, we will get the frequency 

 distribution with respect to the number of pods and it will be 

 exactly the same as that found in the preceding exercise (see 

 table on p. 404) ; likewise, if we add up the frequencies in the 

 vertical arrays, we will get the frequency distribution with 

 respect to length of plants. 



The various steps by means of which the constants for length 

 of plant and those for number of pods were obtained were 

 given in the preceding exercise and need no repetition. They 

 are here secured by the " short method" and are given in the 

 correlation table. We are here concerned with the finding of 

 the constant which will express the degree of correlation between 

 these two characters. 



The only new feature of this correlation table, aside from the 

 method in which the observations are distributed, is the column 

 marked SP. Each element of this column represents the total 

 deviation (from the assumed mean, or guess) of the individuals 

 in each array with respect to both length of plant and number of 

 pods. Thus, taking the first horizontal array, the 5-14 class 

 as regards number of pods, we wish to find how much the in- 

 dividuals in this class deviate from the assumed mean for length 

 of plants. It is found as follows : 



3 individuals each deviated by 30 = 90 

 9 individuals each deviated by 20 = 180 

 3 individuals each deviated by - 10 = - 30 - 300 

 1 individual deviated by + 20 = 20 + 20 



Algebraic Sum = - 280 



All the individuals in this array deviate from the assumed 

 mean for length of plants by the algebraic sum of the total minus 

 deviations and the total plus deviations, which is - 280, as 

 indicated. But each individual in this array with respect to 



