460 TRANSMISSION 



Method of finding correlation coefficient. The method of cal- 

 culating the correlation coefficient (r) is exhibited in connection 

 with the table on page 461, showing a representative case, for 

 convenience continuing the same correlation table already con- 

 structed. Though the method is somewhat complicated it is 

 given in full. 



It is highly important to get at once a general conception of 

 this table and of the method of procedure. All the computa- 

 tions shown except those involved in the column headed 2P 

 have to do only with finding the means and standard deviations 

 of the population with respect to the two characters in question, 

 according to the method fully treated in the last chapter ; that 

 is to say, the columns of figures headed * f L , f L V L , D L , D L 2 , 

 fif>L> f-m firVir* DM D >*> fu'Di? are all self-explanatory to 

 any one familiar with the meaning of ordinary algebraic symbols, 

 and who knows how to find the variability of a population by the 

 methods already given. 



There remains the column of figures headed 2P, which it 

 seems worth while to explain in detail and which is the only 

 special feature in the determination of the correlation coefficient. 

 Each number in this column represents the sum of the products 

 of the corresponding length and weight deviations for every 

 individual in the horizontal array to which the number belongs. 



To show how these numbers are computed, select, for example, 

 the horizontal array marked 10, and we shall show how to find 

 the number 431.0. 



In this case 



10 7.8, the mean, = 2.2 = D L of row 10. 

 Then 



2.2 [i (- 0.7) + i (0.3) + 3 (1.3) + 8 (2.3) + 18 (3.3) 



+ 10 (4.3) + 6 (5.3) + 4 (6.3) + 2 (7.3)] = 431-0. 



All other numbers of the column headed 2P are found in the 

 same way, and the total is written symbolically as *2D L D n ,? 



1 Read "/"sub /r," meaning the frequency of weights ; "/sub w Fsub /^"mean- 

 ing the frequency of weights multiplied by the value in weights ; "/sub /,," mean- 

 ing the frequency of length, etc. 



' 2 The real significance of !LP is best shown by the expression SZ? /./?// , that 

 is, the sum of the products of both deviations of all the individuals in the table. 

 It is written in various ways, but always with the above meaning. 



