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VII. On the Association of Attributes in Statistics: with Illustrations from the 



Material of the Childhood Society, &c. 



R\j G. UDNY YULE, f&i-merly Assistant Professor of Applied Mathematics, University 



College, London. 



Communicated by Professor KARL PEARSON, F.R.S. 

 Received October 20, Read December 7, 1899. 



CONTENTS. 



Page. 



I. Introduction 257 



II. Qeneral relations 261 



III. Association 270 



IV. Probable errors 283 



V. Illustrations (A), miscellaneous 288 



VI. (B), Association of defects in Children and Adults. 297 



I. I NTROD UCTION. 



1. In the ordinary theory of statistical correlation, normal or otherwise, we are 

 always supposed to be dealing with material susceptible of continuous variation, or 

 at least of variation by a considerable number of discontinuous steps'. The correla- 

 tions of lengths or measurements on portions of the body form examples of the first 

 kind ; of numbers of children in families, petals or other parts of flowers, are examples 

 of the second. 



Certain practical cases arise, however, where either no variation is thinkable at all, 

 or else is not measured or possibly measurable. We may class a number of indi- 

 viduals into deaf and not deaf, blind and not blind, imbecile and not imbecile, without 

 attempting to go further (although gradations of deafness, blindness, and imbecility 

 occur), and demand on the basis of the enumeration a discussion of the association* 

 of the three infirmities. Or again the data may be the mortality from some disease 

 with and without the administration of, say, a new antitoxin, the statistics giving 



number who died to whom antitoxin was administered, 

 ,, to whom antitoxin was not administered ; 



* To distinguish it from the " correlation " of continuous variables. 

 VOL. CXCIV. A 258. 2 L 14.7.1900 



