52 



GENETICS IN RELATION TO AGRICULTURE 



change as the other character changes. The general features of such a 

 table are shown in Fig. 24. The intersection of the two means M x and 

 M y , divides the table into quadrants, which are numbered 1, 2, 3, and 

 4. The signs of the deviations from the mean of x and y are opposite 

 in the 1st and 3d, while they are the same in the 2d and 4th quadrants. 

 Now the deviation from M of every individual in the table is V x M x 

 in terms of x and V y M y in terms of y. As these deviations are to 

 be considered relatively, their products are taken. The products of 

 unlike signs are negative, 1st and 3d, and of like signs, positive, 2d and 

 4th. After arranging the x and y individuals in arrays, if the larger 

 number fall in the 1st and 3d quadrants, we learn that there is negative 

 correlation or a tendency for one character to diminish as the other 



FIQ. 25. Interpretation of the correlation table. Shape of 



and amount of correlation. 



'swarm" indicates nature 



increases. If the majority fall in the 2d and 4th quadrants, we conclude 

 that there is positive correlation or a tendency for one character to in- 

 crease as the other increases. If the individuals are uniformly distributed 

 in the four quadrants we find no evidence of interdependence i.e., zero 

 correlation. These typical distributions are illustrated by the three 

 diagrams in Fig. 25. Comparing the two correlation tables (Figs. 22 

 and 23) with these diagrams it is evident that the correlation between 

 yield of plant and number of culms is definitely positive, while the nature 

 of correlation (whether positive or negative) between average height of 

 plant and number of culms cannot be inferred from mere observation 

 of the table but that it is very low indeed is clear from the widely scattered 

 distribution. 



The Coefficient of Correlation. The interpretation of a correlation 

 table is based upon the fact that the table shows deviations with respect 

 to two characters for each individual or class of individuals. We must 

 remember that the x and y deviations of each class from the mean are 

 multiplied in order to understand how the distribution in the table can 

 indicate plus, minus, or zero correlation between the characters. The 

 product of the two deviations for any individual or class is its product- 



