CORRELATION 105 



the heights of the corresponding classes of fathers 

 being read off on the horizontal scale. It will be seen 

 that this series of dots lies nearly in a straight line 

 which is inclined at a certain angle to the horizontal. 



Now if there were perfect correlation between the 

 heights of fathers and sons, and no tendency existed 

 for sons to be more like the general mode of the popula- 

 tion than their fathers are, the inclination of the line 

 obtained in the above manner would be one of 45 

 degrees, as in the case of the line CD which passes 

 through the points at which the values as read off 

 in the vertical and horizontal scales are identical. If, 

 on the other hand, there were no correlation the line 

 would be horizontal, as EF. 



The value taken to represent the amount of correla- 

 tion is the degree of slope of the line AB. This is 

 expressed mathematically as tan a, a being the angle 

 which the line in question makes with the horizontal. 



When there is positive correlation this angle falls 

 between o and 45 degrees, and tan a between o and i. 

 In the present instance tan a is 0*5. This value is 

 known as the coefficient of correlation, and affords 

 the basis of a numerical comparison with other similar 

 coefficients obtained for other characters besides 

 stature, and in the case of other pairs of relatives 

 besides fathers and sons. 



It ought now to be clearly understood that a com- 

 plete resemblance between each class of fathers of a 

 particular stature and the average stature of the 

 corresponding array of sons would be indicated by 

 the close approximation of our plotted points to a 



