256 



MAX LEVINE 

 Y 



X 



The degree of association, or the coefficient of correlation, is 

 then expressed, according to Yule, by the formula 



ad — be 

 ad + be 



If 'ad' is equal to 'be' the coefficient becomes 



(1) 



ad + be °'' ": 

 which indicates that there is no correlation whatever. If either 







b' or 'c' is zero the formula becomes 



ad 



1=1; indicating a 



perfect positive correlation. If 'a' or 'd' is zero then we have 



—be 



-r — = — 1 ; showing a perfect negative correlation. It should be 



observed that an absolute positive correlation exists in reality 

 only if both ' b ' and ' c ' are zero and an absolute negative corre- 

 lation when both 'a' and 'd' are zero. In order to avoid coeffi- 

 cients of 1 or —1 where only one group — 'a', 'b,' 'c;' or 'd'. — is 

 zero. Yule gives the formula 



a (a -h b -i- c -f d) - (a + c) (a + b) 

 ■\/(a-Fc) (b-^d) (a + b) (c + d) 



(2) 



In practice, however, a few strains are almost always found in 

 each of the four groups and Yule suggests the use of the simpler 

 formula (1). Some caution should therefore be employed in in- 

 terpreting coefficients of 1 or —1. 



For this study it was assumed that if the coefficient between 

 two characters is numerically greater than 0.5 they may be 

 regarded as correlated, but if less than 0.3 there is probably no 

 association. A few examples of correlation coefficients actually 

 obtained in the course of this study are given to illustrate the 

 method of calculation. 



