Karl Pearson and David Heron 
201 
and it will be obvious that we are doing Mr Yule no injustice at all. Our 3 in 
175,082 is 557 in 32,527,843 and is far higher than Mr Yule's 96 in 32,527,843 ! 
Why his 96 in over 32 millions might almost consist of the persons who had 
been rendered at the same instant both deaf and blind by accident ! Yet on the 
basis of this result Mr Yule has asserted a "very high association" between deaf- 
mutism and blindness ! 
But, since Mr Yule has no hypothesis as to the nature of his frequency, why 
should not the relation between blindness and deaf-mutism be precisely like that 
of the nature of the variates exhibited in Table VIII ? If this be so, what has 
Mr Yide's coefficient of association told us ? The variates would be actually 
uncorrected, but we should anticipate : 
(i) That extremely bad sight would be associated with extreme deafness — 
this is the above Q = + "78. 
(ii) Extremely bad sight would be associated with great aural acuity. This 
has often been asserted of the blind. Here Q would be high and negative. 
(iii) Extremely good sight would be associated with extremely good hearing, 
i.e. Q would be high and positive. Persons with exceptionally good capacity of one 
sense very frequently have it of another sense. 
(iv) Extremely bad hearing would be associated with exceptionally good 
vision, i.e. Q would be high and negative again. This is quite possible, although 
we have no conclusive evidence on the point. In a small school for deaf-mute 
girls 90 °/ 0 °f the children were found to have normal vision (| or §), none 
had worse than ^g. In a group of children of normal hearing with light hair 
only 69% na cl normal vision and ll'5°/ 0 with vision of ^ or worse. London 
girls give 85°/ 0 > Glasgow 82 °/ 0 and Edinburgh 80 °/ 0 normal vision — all lower 
values than in the case of our small sample of deaf mutes. 
Results (i) — (iv) would hold if there were no correlation between goodness 
of sight and hearing — the average sight of a very deaf person being the same 
as one of normal hearing — -provided the variability in sight of the very deaf were 
less than that of the general population, and the variability in hearing of the very 
blind were also less than that of the general population*. 
Thus given a fourfold table which is based upon continuous variation, if we 
make no hypothesis with regard to the nature of the frequency, we have in fact 
no idea at all of what Mr Yule's coefficients of association and colligation really 
measure. They measure in some form or another deviation from independence, 
it may be true correlation or it may be heteroscedasticity, and divisions taken at 
very slight distances apart may give hopelessly divergent values of Q, of which 
difference of values Mr Yule has given no intelligible interpretation. 
* In the case of our Table VIII, the variability of the horizontal character for the whole population 
= 1-6686, and for the vertical character 1-5979. The variability of the combined two top arrays is 
1-6444, and for the extreme vertical column on the right 1-8166. Had the variabilities of the two sets 
of arrays been the same as those of the general population, the association would have vanished. 
Biometrika ix 26 
