

CORRELATION 463 



Third step. This is the only part of the work that is really 

 new. In doing the second step we found the deviations of 

 the classes from the mean length and mean weight. These are 

 recorded under D L and D iy . For example, in row i we find 

 that 4 ears were each 3 inches long ; that is to say, they 

 deviated 4.8 inches from the mean length taken at 7.8 in- 

 stead of 7.85 in order to save labor. We next take the num- 

 ber in each square of the correlation table and multiply it by 

 the corresponding deviations both in weight and in length, 

 thereby securing a product which is the result of the full num- 

 ber of variates involved and of their deviation in respect to 

 both characters. 



For example, where the column headed 9 ounces and the 

 row labeled 6.5 inches cross each other occurs the number 

 8, which indicates that 8 ears of the population weighed 9 

 ounces and were 6.5 inches long. In other words, these 8 

 ears each deviate 1.7 ounces (row D^, column 9) from mean 

 weight of ears, and 1.3 inches from the mean length (column 

 Z> 7 , row 6.5). Hence for this number 8 we form the product 

 8( i-7)( 1.3) = + 17.68. Without regard to labor, we should 

 find such a product for each number in the correlation table. 

 If now all these products be added and the result divided by 

 the product of the two standard deviations into the number of 

 variates in the total population, we shall obtain the correlation 

 coefficient, or the index of correlation which we seek. 



The systematic way of carrying out this work is to record the 

 results of this operation for each horizontal array under the 

 heading 2P, and then add these results for the arrays to obtain 

 the final result 4947.2, which is symbolically indicated by 

 ^D L D^ or summation D L D^. 



To illustrate the method of calculation a few of the products 

 recorded in column ^P will be shown. 



For example, with 7.8 as the mean length and 10.7 as the 

 mean weight, we have for the array corresponding to length 



4 inches, 



-8.7 x 3 



- 7.7 x 5 

 3.8 x 6.7 x 5 



- 5-7 x i 



This gives 394.4. 



