112 
The Danger of Certain Correlation Formulae 
good agreement and had the Coefficient of Association been used solely in cases 
where the divisions were taken through the means or very nearly so, no very serious 
objection could have been taken to his results as approximations. But this is 
very far from being the case. Instead of restricting the use of the method 
to cases where 
a+b a+c 
were nearly "5, he has applied it to cases where 
N ' N 
a and ai 'e as high as '99978 and has failed to investigate the effect 
of these extreme divisions. 
1-0 
•9 
•8 
•7 
•6 
•5 
■4 
•3 
•2 
•1 
0 
-1 
\ c 
\ 
h 
& 
" Thee 
retical 
value c 
fr" 
r 
/ 
5 15 25 35 45 55 65 75 85 
Ages in Years. 
Fig. 1. Diagram to show the relation between Blindness and Mental Derangement 
at different ages as determined (1) by Mr Yule's Coefficient of Association 
and (2) by Mr Yule's " Theoretical value of r." 
I propose therefore to consider a series of frequency distributions which are 
Gaussian* and to compare the values of the Coefficient of Association found for 
* In doing this I am far from assuming all distributions to be Gaussian. But many are very 
npproximately so, and if Mr Yule's methods lead to absurd results in this case, with what confidence can 
tbiey be applied to others of which we know nothing as to the frequency-distribution ? Mr Yule does not, 
"however, warn us that his coefficients are not to be used when the frequency is approximately Gaussian 
but actually tests them on such material. 
