CORRELATED VARIATIONS. 75 



we must first transmute them into units dependent on 

 their respective scales of variability. We shall thus 

 cause a long or a short cubit and an equally long or 

 short stature, as compared to the general run of cubits 

 and statures, to be designated by identical scale values. 

 The most convenient unit to employ is the value of the 

 probable error of each group. The probable error of 

 the cubit is .56 inch = 1.42 cm.; and of the stature, 

 1.75 inch = 4.44 cm. Therefore each of the measure- 

 ments of the cubit must be transmuted into terms of a 

 new scale, in which each unit = .56 inch, and each of 

 the measurements of the stature into those in which 

 each unit 1.75 inch. After this has been done, we 

 shall find that on an average each deviation in the 

 stature of say 1 unit from the mean is not accompanied 

 by a similar deviation of 1 unit in the cubit, but by 

 only .8 of a unit. Conversely it is found that in a 

 similar manner each deviation in the cubit of 1 unit 

 from the mean is accompanied by only .8 of a unit of de- 

 viation in the stature. The degree of correlation, or r, 

 between the one organ and the other, is therefore said 

 to be .8. If the correlation had been perfect, then this 

 r would have been equal to 1, and if it had been entirely 

 wanting, then it would have been 0. Comparison with 

 other data shows that a correlation of .8 is a high one, 

 not often surpassed. The other correlation constants 

 determined by Galton are the following: 



MEAN r. 



Stature and head length, 35 



Stature and middle finger, 7 



Middle finger and cubit, 85 



Head length and head breadth, 45 



Stature and height of knee, ..... .9 



Cubit and height of knee, 8 



