Volume II FEBRUAIIY, 1903 No. 2 



NOTES ÜN THE THEORY OF ASSOCIATION OF 

 ATTRIBUTES IN STATISTICS. 



By G. UDNY YULE. 1 ... >.1>Y 



CONTENTS. BOT.^NICAL 



GARDEN 



Page 



IntrodiR'tory ............. 121 



1. Notation ; terminology ; tabulation, etc 122 



2. Consistence and iuference 124 



3. Association 125 



4. On the theory of coraplete independence of a seriea of Attributes . . 127 



5. On tlie fallacies that may be caused by the mixing of distinct records . 132 



The simplest possiblo form of Statistical Classification is " division " (as the 

 logicians term it) " by dichotomy," i.e. the sorting of the objeets or individuals 

 observed into one or other of two mutually exclusive classes according as they do 

 or do not possess some character or attribiite ; as one may divide meii into sane and 

 insane, the members of a species of plauts into hairy and glabrous, or the members 

 of a race of animals into males and female.s. The raere fact that we do eniploy 

 such a Classification in any case must not of course be held to imply a natural and 

 clearly defined boundarybetween the two classes; e.g. sanity and insanity, hairiness 

 and glabrousness, may pass into each other by such fine gradations that judgments 

 may differ as to the class in which a given individual should be entered. The 

 judgment must however be finally decisive; intermediates not being classed as 

 such even when ob.served. 



The theory of statistics of this kind is of a good deal of importance, not 

 merely because they are of a fairly common type — the statistics of hybridisation 

 experiments given by the followers of Mendel may be cited as recent examples — 

 but because the ideas and conceptions required in such theory form a useful 

 introduction to the more complex and less purely logical theory of variables. The 

 classical writings on the subject are those of De Morgan*, Boole f and JevonsJ, 

 the method and notation of the latter being used in the following Notes, the first 

 three sections of which are an abstract of the two memoirs referred to below§. 



* Formal Logic, ehap. vm., " Du the Numerically Definite Syllogism," 1847. 



t Amdysis of Logic, 1847. Laics of Thought, 18.54. 



t " On a General System of Numerically Definite Reasoning," Memoirs of Manchester Literanj and 

 Philosophical Society, 1870. Eeprinted in Pure Logic and other Minor iVorks, Macmillan, 1890. 



§ "On the Association of Attributes in Statistics," Phil. Trans. A, Vol. 194 (1000), p. 2.57. " On 

 the theory of Consistence of Logical Class Freijuencies," Phil. Trans. A, Vol. 197 (1901), p. 91. 

 Biometrika ii 16 



