120 Relationsliip of Intelligetice to Size and Sha^je of Head 
school children, all the measurements were I'educed to a standard age of 12 by aid 
of the average growth curves. The substantial legitimacy of this process is 
demonstrated by the close agreement of the results with those for the Cambridge 
graduates. In the Appendix Tables XIV — XXIV give the tabulated measurements. 
These tables differ from those published in the preliminary papers, in that they no 
longer give mere fourfold divisions but contingency classifications showing the 
total distributions of head measurements for each mental grade. The method of 
reduction used throvighout this part of the memoir was that of the correlation 
ratio 77*. 
This ratio ?; is a true measure of the divergence from independence of the 
two variables, whatever be the nature of the regression. If the regression be 
really linear, 7] passes over into the well-known correlation coefficient. The four- 
fold tabulation and the discovery of the correlation coefficient"!" were adopted 
in the preliminary investigations already published. 
In the accompanying Table VIII the correlations between shape and size 
of head are given, and Fig. 5 shows the same results exhibited in a graphical 
form. 
TABLE VIII. 
Correlation Ratio between Shape and Size of Head and Ability I. 
Intelligence and 
Cambridge Graduates 
School boys at Twelve 
Years 
School girls at Twelve 
Years 
Cephalic Index 
Length of Head . . . 
Breadth of Head ... 
Auricular Height ... 
(loii) _ .Qg^ ^ 
-111 + -020 
-097+ -021 
(2345) _. 041 + -014 
''58 -139+ -014 
™ -109+ -014 
(-9°) -073 +-014 
l'"f| -067+ -014 
rf -084+ -014 
-113+ -014 
™ -0.55+ -014 
Having regard to the magnitude of the probable errors, it is obvious that : 
(a) The correlations are, with the exception of the cephalic index, in every 
case uniformly of one sign and sensible. 
(b) They are so small that they are in every case of no service for the purposes 
of prediction. 
(c) Within the limits of the probable error, the results for adults and for 
school children are in good agreement. The divergences for each character 
within the three populations are practically within the limits assigned by the 
probable error of their differences. 
These conclusions are based upon a far larger number of measurements than 
any hitherto published, and are, I think, convincing as to the small part played by 
head size in determining the grade of intelligence. I have shown in another 
* Drapers^ Company Research Memoirs, Biometric Series II. Dulau and Co. 
t Phil. Tranx. Vol. 19.5 A, pp. 1—47. 
J The numbers in brackets give populations dealt with. 
