In judging these tables we make the important assumption that the teacher's estimate of the ability of a boy at a given age is approximately 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.
