I.—NOTATION AND TERMINOLOGY. J 
differ as to the class in which a given individual should be 
entered. The possibility of uncertainties of this kind should 
always be borne in mind in considering statistics of attributes: 
whatever the nature of the classification, however, natural or 
artificial, definite or uncertain, the final judgment must be de- 
cisive ; any one object or individual must be held either to possess 
the given attribute or not. 
5. A classification of the simple kind considered, in which each 
class is divided into two sub-classes and no more, has been termed 
by logicians classification, or, to use the more strictly applicable 
term, division by dichotomy (cutting in two). The classifica 
tions of most statistics are not dichotomous, for most usually a 
class is divided into more than two sub-classes, but dichotomy is 
the fundamental case. In Chapter V. the relation of dichotomy 
to more elaborate (manifold, instead of twofold or dichotomous) 
processes of classification, and the methods applicable to some 
such cases, are dealt with briefly. 
6. For theoretical purposes it is necessary to have some simple 
notation for the classes formed, and for the numbers of observa- 
tions assigned to each, 
The capitals 4, B, C, . . . will be used to denote the several 
attributes. An object or individual possessing the attribute 4 
will be termed simply 4. The class, all the members of which 
possess the attribute 4, will be termed the class 4. It is con- 
venient to use single symbols also to denote the absence of the 
attributes 4, B, C, . . . We shall employ the Greek letters, a, 
By v» -.. Thus if A represents the attribute blindness, a 
represents sight, i.e. non-blindness; if B stands for deafness, 8 
stands for kearing. Generally “a” is equivalent to “non-A,” or 
an cbject or individual not possessing the attribute A ; the class a 
is equivalent to the class none of the members of which possess the 
attribute A. 
7. Combinations of attributes will be represented by juxta- 
positions of letters. Thus if, as above, 4 represents blindness, B 
deafness, AB represents the combination blindness and deafness. 
If the presence and absence of these attributes be noted, the four 
classes so formed, viz. 4B, 4f3, aB, af3, include respectively the 
blind and deaf, the blind but not-deaf, the deaf but not-blind, and 
the neither blind nor deaf. If a third attribute be noted, e.g. in- 
sanity, denoted say by C, the class ABC, includes those who are 
at once deaf, blind, and insane, 4 By those who are deaf and blind 
but not vnsane, and so on. 
Any letter or combination of letters like 4, AB, aB, ABy, by 
means of which we specify the characters of the members of a class, 
may be termed a class symbol. 
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