ON A NEW METHOD OF DETERMINING CORRELATION 
BETWEEN A MEASURED CHARACTER A, AND A 
CHARACTER B, OF WHICH ONLY THE PERCENTAGE 
OF CASES WHEREIN B EXCEEDS (OR FALLS SHORT 
OF) A GIVEN INTENSITY IS RECORDED FOR EACH 
GRADE OF A. 
By KARL PEARSON, F.R.S. 
(1) As an example of the class of cases to which the method of this paper 
applies I instance that we might be given the ages of candidates for a given 
examination, and the number of failures at each age, without the individual 
marks ; from these data we might desire to correlate capacity and age. Or, again, 
we might be given the percentage of first convictions for each age group of the 
community, and the problem might be to determine the relation between age and 
the tendency to crime as judged by conviction. Or, age being put on one side, we 
might desire to correlate any psychical character with anthropometric characters, 
e.g. the cephalic index in children as a more or less marked racial character with 
their conscientiousness or shyness, measured by the number of shy or conscien- 
tious children at each value of the index. 
If the non-measurable, or at least unmeasured character, be classed into a 
considerable number of groups there is no doubt that the most satisfactory method 
to adopt is that of the correlation ratio*. The cases we have in view here, how- 
ever, are those in which no such series of groups has been made, or possibly can be 
made. As a rule we have, hitherto, fallen back in such cases on a fourfold table 
method — that is to say, we have been tacitly compelled to drop any advantage 
that arose from one character having a measured value. Further the result was 
not unique, depending to some extent on where the division of the measured 
character was made. The present method is unique, it involves only the discovery 
of two means and one standard deviation (no product moment, no second standard 
deviation and no complicated equation having to be worked out); it is in fact 
singularly brief. It is only for one determination that we have to assume that the 
Gaussian frequency distribution may be applied with sufficient practical accuracy. 
This defect (though, I think, to a minor extent) it shares with the fourfold table 
method ; but because it does, the method will serve in the cases to which both can 
be applied as a useful control method. 
* Pearson : " On the Theory of Skew Correlation." Drapers Research Memoirs (Dulau & Co), 
