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 opposite, the 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, the heights 
