THE STATISTICAL STUDY OF VARIATION 



559 



populations. Opinion differs as to the significance of these findings. 

 The more optimistic evolutionists look upon such instances as that of 

 Bateson's earwigs as visual demonstrations of a species actually split- 

 ting up into two or more species. It seems quite likely that one of 

 these types is a successful mutant type that has not fully segregated 

 itself as a true species from the parent-type. Another view of the 

 significance of bimodal curves is that the condition results from hybridi- 

 zation and that the bimodality is the result of the segregation of 

 dominant and recessive types. 



Fig. 93. — Bimodal polygon plotted from data on the earwig. Mean types 

 (Xf ) indicated above corresponding modes. Numbers below the base line indicate 

 length of pincers in millimeters. (From Bateson and Johannscn.) 



THE COEFFICIENT OF CORRELATION 



Only one more biometrical constant need be mentioned here: the 

 "coefficient of correlation." It is often necessary to discover the 

 exact relation that exists between two sets of variables in order to 

 discover whether they are totally independent or partially correlated 

 with each other. For example, we have found that there is a close 

 correlation between stature and head length in man, also between 

 color of hair and color of eyes; but it is very important to be able to 

 reduce the degree of correlation to a simple arithmetical constant. 

 This is called the "coefficient of correlation" (commonly expressed 

 as r xy , where x is one variable and y the other). The formula for com- 

 puting r xy is as follows: 



xy 



2 (d^dy) 



11 



<T X <Jy 



