io8 BIOMETRY 



and both are the same as the mean height of the general 

 population, the coefficient of regression is simply equal 

 to the reciprocal of the correlation coefficient between 

 fathers and sons. In actual practice this condition is 

 seldom realized, and it is then necessary to use a more 

 elaborate method in order to determine the value of 

 the regression coefficient. 



Professor Pearson has extended the idea of correla- 

 tion to the case of characters which are not capable of 

 exact quantitative measurement. This extension is 

 based upon the assumption that such characters follow 

 a normal law of distribution in their variation, just in 

 the same way as such a character as human stature was 

 found to do. There is considerable doubt as to how 

 far this assumption is justified, so that at the outset 

 we may feel disposed to attach less importance to the 

 actual values arrived at in this way than we should in 

 the case of characters which can be shown to vary 

 normally. The method of calculation actually em- 

 ployed involves somewhat complicated mathematical 

 processes, but on Professor Pearson's authority we 

 may assume both the validity of the method and the 

 accuracy of the results obtained so far as the actual 

 process of computation is concerned. For the purpose 

 of making the necessary calculations the data were 

 arranged in such a form as in the table on p. 109. 



By the suitable treatment of these figures the 

 value 0-45 was obtained as representing the coefficient 

 of correlation between sire and filly. 



The amount of reliance which is to be placed in the 



