Karl Pearson and David Heron 
273 
needful arithmetic, tells us that the index of correlation between stature and rent 
is perfect* ! 
(F) Eye-Colour Data of Pearson. 
We now come to the eye-colour data. These are the only cases we have so 
far worked out in which the variability of Q is at all comparable with that of 
tetrachoric r t , and the reason is not very far to seek. We have already pointed 
out that the true difficulty in these eye-colour tables appears to lie in lumps 
of excess frequency in or near the corner cells of the quadrants of less frequency 
and that thus the material is heterogeneous in character. We think it quite 
probable that this is due to the inclusion of really senile fathers on the one hand 
and of infant sons on the other, or of pairs of brothers or sisters one of whom is 
an infant. In this manner eye tints which are originally, or will become, mediocre 
in colour may be classified as very light. The record which Sir Francis Galton 
provided gave no ages ; the original data are now in the possession of the Galton 
Laboratory and it is proposed to reconsider both these and the Huxley Lecture 
data for eye-colour f, paying attention to change of eye-colour with age. This 
investigation will necessarily take a considerable time and it might be wiser 
to await its conclusion before entering further on this topic. But we should no 
doubt be told that we were omitting just those cases that appeared favourable 
to Mr Yule's association coefficient, and accordingly we have included the eye- 
colour data here. The table on p. 274 gives the Brother-Brother coefficients for 
16 divisions. 
Now this is a symmetrical table and Mr Yule reckons the diagonal coefficients 
once, and the repeated coefficients twice, but we are doubtful of the accuracy of 
this process. Such a symmetrical table leads to exactly the same results from 
symmetrically placed divisions, and it is not clear why double weight should be 
given to such a division as 2- — 3 and 6 — 7 because as the table is written out 
it occurs twice. It seems to us that the diagonal values and all on one side of 
them are the only independent coefficients ; we have lost the independence of the 
coefficients in the cells symmetrically situated with regard to the diagonal by 
the very process of adding the tables for First Brother in terms of Second Brother 
* A. Niceforo, "Contribution a l'etude des correlations entre le bien-etre economique et quelques 
faites de la vie demographique," Journal de la Societe de Statistique de Paris, 52 Ann^e (1911), 
pp. 322 — 341. Professor Niceforo studies "correlations" by aid of the coefficient of association, 
which he applies to the following continuous variates : stature, rent, probable income, numbers of 
illiterates, of insanitary dwellings, of paupers, of pauper funerals, of workers, size of families, numbers 
of cubic feet of air space, of inhabitants to the acre, special death-rates from all sorts of diseases, 
general death-rates and birth-rates etc., etc. We believe that the whole of this work must be redone. 
Even if a rough estimate had been required, Mr Yule's coefficient should not have been used, but the 
division made at the median values and Sheppard's formula for tetrachoric r t adopted. There is not 
even the excuse of apparent discreteness in any of Professor Niceforo's attributes. 
t Pairs of siblings in the same school are much more nearly of an age than any pair between the 
ages of 5 and 15 taken from the population of school children. While the head-measurements were 
corrected for age, the hair and eye colours were not, and probably the changes are more important than 
we believed at that date. 
Biometrika ix 35 
