BIOMETRY 67 



In the table the entries would show a tendency to group 

 themselves about the diagonal, but there would be a con- 

 siderable scattering of entries in squares not lying in the 

 diagonal. Compare Tables 1 and 3. 



If men in general did 7iot increase in weight as they increase 

 in height, but actually grew lighter as they grow taller, then 

 we should find a negative value for the coefficient of correla- 

 tion. Cases of this kind are occasionally met with, but they 

 are of no importance since by rearrangement of the correla- 

 tion table (as by reversing the order of the grades for one 

 character) a negative result may always be converted into a 

 positive one of like magnitude. The essential thing, which a 

 coefficient of correlation does, is to show whether two ob- 

 served phenomena are or are not causally related to each 

 other. Any result other than indicates that the two sets 

 of phenomena are so related, and the size of the coefficient 

 indicates the extent to which they are causally related, up to 

 a value of + 1 which would indicate that they are due to 

 identical causes. 



In biometry the correlation table has found two principal 

 uses (1) to show what parts or processes of an organism 

 vary in unison and to what extent they so vary and (2) to 

 measure heredity. Examples of the first use are the relation 

 between height and weight in man already discussed and 

 the relation between one skeletal dimension and another, 

 as skull length and femur length, which in rabbits have a 

 correlation of 0.76, or the lengths of femur and humerus, 

 which in rabbits show a correlation of 0.86. See Table 3. 

 The correlation values for corresponding bone measurements 

 in men are very similar. If the correlation between two 

 parts is known, it is possible from a knowledge of the 

 magnitude of one of them to predict the magnitude of the 

 other, with an accuracv indicated bv the coefficient of corre- 

 lation. If for instance the correlation between femur and 

 humerus is 0.86 and I know the femur length of an individ- 

 ual, I can estimate his humerus length with an accuracy of 

 about 86 per cent. 



