Pearl, Intelligence and Size of Head. 



195 



These values are in very good accord and we may hence conclude 

 that with this grouping 



Ci=C2=r=o.i4 

 It has been shown by Pearson that it is likely that the probable 

 error of a contingency coefficient will be less than 



2 X .67449^' 



For C = .1410 and N = 935 the value of the above expression 

 is ± .0432. Assuming that this in any event does not exceed the 

 true value of the probable error we conclude that the data in 

 Table II exhibit a positive correlation between general intelli- 

 gence and head circumference expressed by a coefficient of 



r = .i4±.04. 



In other words, the chance that such a system of frequencies as 

 that given in Table II should arise if, in the population under 

 consideration, there were no correlation between head size and 

 intelligence would be, so far as we can judge, not greater than i 

 in 1250. It seems reasonable to conclude, therefore, that this 

 material does show a sensible correlation between these characters. 

 We may, however, test the matter further. From the data 

 furnished by Table I it is possible to form a fourfold table, and 

 evaluate the coefficient of correlation directly and with a known 

 probable error by the method given by Pearson.^ Such a four- 

 fold table is given as Table III. 



table III. 

 Correlation Between Intelligence and Head Circumference. 



Intelligence. 



^Phil. Trans., Vol. 195 A., pp. 1-46. 



