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, and 
M,, 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, — M, 
in terms of z« and V, — M, in terms of y. As these deviations are to 
be considered relatively, their products are taken. The products of 
unlike signs are negative, lst 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 Ist and 3d quadrants, we learn that there is negative 
correlation or a tendency for one character to diminish as the other 
Fig. 25.—Interpretation of the correlation table. Shape of ‘‘swarm’’ indicates nature 
and amount of correlation. 
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 7.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 « 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- 
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