Ability with the Size and Shape of the Head. 339 



Li judging these tables we make the important assumption that the 

 teacher's estimate of the ability of a boy at a given age is approxi- 

 mately correct if applied to him when 12 years old. There will of 

 course be exceptions to this rule, but they will hardly be numerous 

 enough to invalidate the results drawn from such broad classifications 

 as we are here dealing with.* 



These results confirm entirely the conclusions we have drawn from 

 the Cambridge statistics. There is a non-significant correlation 

 between dolichocephaly and ability ; there are very small correlations 

 between length and breadth of head and ability. The ability and 

 length correlation here is about what the ability and breadth correla- 

 tion was in the Cambridge case, and rice versa. Hence we cannot 

 assert that either length or breadth is dominant in the case of ability. 



SunwHtri/. If we sum up the conclusions which can be drawn from 

 our present material, I think they would run as follows : 



We have taken two standards of ability : (i) a youth's view of his 

 own capacity (doubtless influenced by the opinions of his parents and 

 teachers), determined by whether he works for a pass or honours degree ; 

 (ii) the teacher's view of the child's capacity. In neither case is there 

 a sensible relation between ability and shape of the head as judged by 

 the cephalic index. 



In both cases there is a small correlation between the size of the 

 head as judged by both length and breadth and the individual's ability. 

 The mean of the values found gives r = O0649 for length and 

 ability and 0'0647 for breadth and ability, or taking these as the same, 

 we may say that the correlation between size of head and ability is 

 0-0648, practically 0-065. 



Let us examine this numerically to realise better its degree of 

 significance. Consider the class of people who have an ability which 

 occurs only in 2 per cent, of the population a fairly high standard. 

 Let // be their grade of intelligence and (r the standard deviation of 

 intelligence ; so that 2 per cent, of the population have an intelligence 

 differing from the mean by h or more. Then to find li/a- we have : 



1 . 



70" - 



v/2ir, /,/,. 



whence, by tables of the probability integral : 



hfa- = 2-05375. 



Let y be the mean size of head of these exceptionally able people 

 and o-' the standard deviation of size of head r = 0*065, and N = 

 total population. Then : 



* As a teacher, I am continually struck by the accordance between one's general 

 appreciation of a student's power not necessarily on an examination-room scale 

 and his after-achievement in life. 



