24 KARL PEARSON 



deformities and in other cases to which Mr Yule, and — I regret to say — continental 

 anthropologists and economists on his authority are now applying it*. 



(v) The value of Vp seems to me based on a scientific conception. We agree to 

 measure the closeness of association by the improbability that the material could have 

 arisen from a random sample of unassociated variates. But this probability offers no 

 easily apprehensible mental scale. Accordingly we determine to replace our improba- 

 bihties by correlations which would have been equally unlikely to arise from a random 

 sample of uncorrelated material. The choice then to be made is one of a correlation 

 scale. The probability of any r can be determined in terms of the standard deviation 

 of r for uncorrelated material. But what standard deviation shall we select 1 In 

 order that our results shall agree fairly closely with the results for Gaussian distribu- 

 tions we select our arbitrary standard deviation, and so our scale, to be that of a zero 

 correlation for a fourfold Gaussian table with its variates divided in the same 

 proportions as in the actual material. If we estimate our probability of independence 

 on this correlation scale, we see that the values of r^, the probability correlation, 

 never differ very widely from those which would be obtained by supposing the four- 

 fold table to represent a Gaussian frequency distribution. In other words, even 

 when a table is non-Gaussian, or cannot be thought of as representing continuously 

 varying material at all, so that r^ ceases to have any meaning as connected with 

 regression or array variation, still its value has a perfectly definite and new 

 significance : it measures reasonably closely the improbability that the sample 

 could have arisen from non-associated material ; it is a measure of association on 

 a probability scale. 



(vi) By aid of Table V and of Table IV, or the accompanying abac, Vp, or 

 approximately r^, this measure of the improbability of independence on a standard 

 correlation scale can be found for any fourfold table in a few minutes. The extension 

 of the fundamental idea of this paper to 3 x 3 tables suggests itself, and I hope shortly 

 to publish a supplementary paper on that point. 



* I am sorry to animadvert thus strongly on the work of an old pupil and colleague, but I consider 

 that the association coefficient never had more than formal logical interest, and that to try to resuscitate 

 it in practical statistics is to check the advance of modem scientific methods. Since this paper was 

 printed, I have seen a memoir by Mr Yule in type, which is shortly to be issued in the Journal of the 

 Royal Statistical Society. In that paper he defends, on what appear to me to be wholly inadequate 

 grounds, the use of his Coefficient of Association and introduces what he terms a " Colligation Coefficient " 

 — a very old friend with a new name. A reply, at length, to that memoir will appear in the forthcoming 

 number of Biometriha. 



