122 Oh the Theorij of Association 



1. Notation ; terminology ; relations between the class frequencies ; tahulation. 

 The Dotation used is as foUows * : 



N = total number of observations, 



{A) = no. of objects or individuals possessing attribiitc A, 

 (a) = „ „ not possessing attribute A, 



{AB) = „ „ possessing both attributes A and B, 



{Aß) = „ „ „ attribute A btit not B. 



{aB) = „ „ „ attribute B but not A, 



{aß) = „ „ not possessing either attribute A or B, 



and so on for as many attributes as are specified. A class specified by n attributes 

 in this notation may be termed a class of the «th order. The attributes denoted 

 by English capitals may be termed positive attributes, and their contraHes, 

 denoted hy the Greek letters, negative attributes. If two classes are such that 

 every attribute in the one is the negative or contrary of the corresponding 

 attribute in the other they may be tcnucd contrary classes, and their frequencies 

 contrary frequencies; {AB) aud {aß), {ABy) aud {aßC) are for instance pairs of 

 contraries. 



If the complete series of frequencies arrivcd at by notiug n attributes is being 

 tabulated, frequencies of the same order should be kept together. Those of the 

 same order are best arranged by taking separately the set or " aggregate " of 

 frequencies, derivable from each positive class by substituting negatives for one or 

 more of the positive attributes. Thus the frequencies for the case of three 

 attributes may conveniently be tabulated in the order — 



Order 0. iV 



Order 1. {A), {a) : {B),{ß): {G), {y) 



Order 2. {AB). {Aß), {<xB), {aß): {AG), {Ay). {aO), (07): {BC), {By),} (1). 



{ßC), {ßy) 

 Order 3. {ABC), {oBC), {AßC), {ABy), {aßC), {aBy), {Aßy), («ySy) 



But since all frequencies are used non-exclusively, {A) denoting the frequency 

 of objects possessing the attribute A with or without others and so forth, the 

 frequency of any class can ahvays be expressed in terms of the frequencies of 

 classes of higher order ; that is Do say we have 



N =(yl)+(a) = (5) + (/3) = etc. 



= {AB) + {Aß) + {aB) + {aß) = etc. 

 {A) = {AB) + {Aß) 



= {ABC) + {ABy) + {AßC) + {Aßy) = etc. 



* I have Bubstituted small Greek letters (or Jcvons' italics. Italics are ratlier troublesome wben 

 speaking, as one has to spell out a «ronp likc AhcDE, "big A, little b, little c, big D, big JE." It 

 is simpler to say .IßyDE. The Greek becomes moro troublesome whcn many lettera are wantcd, 

 owing to the nou-corrospondence of the alphabets, but this is not ofteu of consequence. 



.(2). 



