Pearl, Intelligence and Size of Head. 197 



what greater than the coefficient of correlation from Table III 

 while at first thought it might be supposed that according to the 

 theory of contingency they ought to be equal. This, however, 

 does not follow, because the division of the intelligence scale in 

 Tables I and III is different from what it is in Table II on which 

 the contingency coefficient is based. In Tables I and III the 

 middle class of Table II is divided. Now, I think it will be ad- 

 mitted that there would be far more doubt in the mind of the 

 classifier as to whether a given individual ought to be placed in 

 class Ila or lib of Table I, than as to whether he should be placed 

 in the "gut" class of Table II. But any errors made in the assort- 

 ing of individuals into the two middle classes of Table I, will 

 affect the coefficient of correlation deduced from the fourfold 

 table, while, of course, they would in no way affect the contin- 

 gency coefficient. Consequently I am inclined to think that in 

 this case the contingency coefficient is a truer measure of the real 

 degree of correlation. In any event, the difference between the 

 contingency coefficient and the correlation coefficient from the 

 fourfold table is only of the order of the probable error of the 

 latter. 



To sum up, then, we find by analyzing fairly copious statistics 

 forming a homogeneous sampleof the males in the poorerclasses of 

 the Bavarian population that there is alow, but still sensible, posi- 

 tive correlation between the horizontal circumference ofthe head and 

 general intelligence. This result 'appears to be of considerable in- 

 terest. The only previous statistics of a similar nature are Pear- 

 son's data^ for Cambridge undergraduates, and English school 

 children. 



In order to show how these results compare with those of the 

 present paper I have taken the mean of the nine coefficients for 

 the correlation of absolute head dimensions (length, breadth and 

 auricular height) with intelligence which Pearson has given. 

 The value is .0736. All of the nine coefficients are positive.^ 

 To these values we are now able to add the coefficient for the 



^Loc. cit. 



^I am informed by Professor Pearson that since the preliminary papers here cited were published, 

 the material on which they were based has been worked over anew by the contingency method. The 

 result has been to give slightly higher values to some of the coefEcients and a generally smoother sys- 

 tem. These new values are thus in even better accord with the coefficient found in the present paper 

 for intelligence and horizontal circumference. As these new values are to be published shortly, it 

 seems undesirable to reproduce in detail the coefficients given in the preliminary papers. 



