280 MR. G. UDNY YULE ON THK ASSOCIATION 



31. But besides these partial coefficients there are others that we may form, where 

 we deal with the association between two groups of qualities or attributes, or between 

 a single attribute and a group. These coefficients arise naturally out of the total 

 coefficients ; for in any total coefficient a single letter may really represent an 

 aggregate of qualities that we may more completely denote by a group of letters. 

 Thus A may represent deaf-mutism, C imbecility, and | AC | the association between 

 deaf-mutism and imbecility ; but if we amplify the notation and use A = deafness, 

 B = dumbness, C = imbecility, the association between deaf-mutism and imbecility 

 will be represented by 



. _ (ABC) (a/fry) - (a/8C)(AB7) , } 



~ 



This | AB . C | is quite distinct from | AB | C | . The latter measures the association 

 between A and B in a group of individuals all possessing C. The former measures 

 the association between C and the compound attribute AB. 



A more general form of association coefficient is such a " group coefficient with 

 the universe specified, i.e., a partial group coefficient. For example 



(ABODE) (q^ySE) - (aCDE) (AB 7 8) 

 " ( ABODE) (a/3 7 SE) + (aCDE) ( AB 7 SE) 



The, Method of Sei*ial Chances. 



32. There is a very common method of handling such associations as we have 

 here to deal with, more especially where it is desired to discuss the association of 

 some one attribute A with a series of others B, C, D, &c. The chances (AB)/(B). 

 (AC)/(C), &c., are simply tabulated in order of magnitude, and the attribute X for 

 which the chance of X being A, or (AX)/(X), is greatest is held to be the " most 

 important cause of A." 



The method seems to have l>een first brought forward, as a definite statistical 

 method, by QUETELET, in a pamphlet published in 1832, ' Sur la possibility de mesurer 



