12 EMPIRICAL STUDIES OF MEASUREMENT 



The gross variabilities often increase as we would expect with 

 higher central tendencies, though by no means always. Seven out 

 of ten do so, giving a median value of 109.2 instead of 100. The 

 Pearson coefficient of variation makes too much of a deduction for 

 an increase in the amount of the central tendency in all but three 

 cases, giving a median value of 90.1 instead of 100. The square root 

 deduction, with a median value of 97.5, makes the least error of any 

 one single method. These facts alone disqualify the so-called * coeffi- 

 cient of variation' as a means of comparing variabilities. But more 

 detailed studies of the cases of length of finger, span and stature will 

 be still clearer. 



The facts for length of left middle finger are as given in Table VI. 



TABLE VI. 



RELATION OF AMOUNT OF VARIABILITY TO AMOUNT OF CENTRAL TENDENCY. 

 FINGEE LENGTH. (Biometrika, Vol. I., p. 216) 



Array. 

 1 

 2 

 3 

 4 

 5 



9 

 10 

 11 

 12 

 13 

 14 

 15 

 16 

 17 



In the case of finger length increase in the amount of the central 

 tendency does not imply an appreciable increase in the amount of 

 variability. No allowance is needed. 



In the case of span it would be equally absurd not to make an 

 allowance and one as great or nearly as great as the Pearson method 

 makes. For the preliminary study of the variability of span re- 

 ported in Table V. is confirmed by the facts in the case of three 

 other span series. These facts (given in Table VII.) abundantly 

 prove that the influence of the amount of the central tendency on the 

 amount of the variability follows totally different laws in the case 

 of span ana of ringer length. 



