104 BIOMETRY 



In the ' correlation table ' given on p. 102 a 

 purely imaginary illustration there are tabulated the 

 statures of 4,503 fathers, and those of one son of 

 each of them. Thus 14 fathers, each 62 inches high, 

 are supposed to have had 14 sons, whose heights are 

 given in the first column. The series of heights of sons 

 corresponding to a particular class of fathers is known 

 as an array. Thus each column of the table represents 

 an array of sons, and similarly each line represents an 

 array of fathers. The mode of each array of sons is 

 given in the bottom line of the table. 



Now if sons were on the average exactly the same 

 height as their fathers, the modal value of each array 

 of sons would be the same as the height of the corre- 

 sponding class of fathers. If, on the other hand, there 

 were no correlation between the heights of sons and 

 those of their fathers the mode of every array of sons 

 would be the same, and this value would be identical 

 with the mode of the heights of all the sons taken 

 at once. The actual result is found to be intermediate 

 between these two possible extremes. Thus we see 

 that sons tend to be like their fathers in respect of 

 stature, but not exactly like, and if the example given 

 were a real one the fundamental fact of a positive 

 resemblance or correlation between the statures of 

 fathers and sons would at once be clearly established. 



The way in which a numerical value is attached to 

 this correlation can be shown graphically. 



In the diagram shown in Fig. 9, tfife dots indicate 

 the values of the modes of the several arrays of sons 

 as read off on the vertical scale to the left of the figure, 



