OF ATTRIBUTES IN STATIST' 



Thus 



(A) = (AB) + (A/3) 



= (ABC 1 ) + (ABy) + (A/8C) + (A/By) 



= (ABCD) + (ABCS) + (AB y I>) 4- (AByS) 



+ (A#Jl>) + (A0CS) 4- (A/8yD) 4 (A,8yS) 

 = &c. 



and also if (U) be the total frequency (total number of observations, total number in 

 the "universe of discourse ") 



(U) = (A) + (a) = (B) 4- 08) = (C) + (y) = &c. 



The whole of JEVONS' method, so far as applied to purely numerical problems, depends 

 on the use of equations of the above form, or the expansion of groups in terms of 

 their sub-classes. 



4. We shall adopt the following conventions. When requiring to distinguish the 

 qualities denoted by English letters from those denoted by Greek, we shall call the 

 former positive qualities, the latter negative. A group in which all the qualities 

 specified are positive will be called a positive group, and conversely. 



A group specified by n qualities (positive or negative) will be termed an nth 

 order group. 



To distinguish the nth order groups in n variables from 7Jth order groups 

 formed from a larger number of variables, we shall refer to the former as " ultimate" 

 groups. 



Two groups such that each quality in the one is the negative (or contrary) of 

 each quality in the other will be termed contrary groups, and their frequencies con- 

 trary frequencies. Thus 



ABCD 



aBC 



ayDE ABCSe 



are pairs of contraries. The case where the frequencies of contrary groups are equal 

 is of some importance. This will be called the case of "equality of contraries." 



Consider, for example, the case of normally correlated continuous variables. If 

 A denote the class in which some quality is above the average, a. the class in which 

 the same is below* average, and so on with B, /3, &c., then from the symmetry of 

 the surface we must have 



* Logically "not above average"; but we take the average as a mathematical point, so that there are 

 no individuals with exactly average qualities. 



2 L 2 



