11T.—ASSOCIATION. 9 
A and B are said to be negatively associated or, more briefly, 
disassociated. 
The student should notice that these words are not used 
exactly in their ordinary senses, but in a technical sense. When 
A and B are said to be associated, it is not meant merely that 
some A’s are B’s, but that the number of A’s which are B’s exceeds 
the number to be expected if A and B are independent. Similarly, 
when 4 and B are said to be negatively associated or disassociated, 
it is not meant that no 4’s are B’s, but that the number of A’s 
which are B's falls short of the number to be expected if A and B 
are independent. *“ Association” cannot be inferred from the mere 
fact that some A’s are B’s, however great that proportion ; this 
principle is fundamental, and should be always borne in mind. 
6. The greatest possible value of (4B) for given values of 
WN, (4), and (B) is either (4) or (B) (whichever is the less). When 
(4B) attains either of these values, 4 and B may be said to be 
completely or perfectly associated. The lowest possible value of 
(4B), on the other hand, is either zero or (4)+ (B)— N (which- 
ever is the greater). When (4.5) falls to either of these values, 
4 and B may be said to be completely disassociated. Complete 
association is generally understood to correspond to one or other 
of the cases, “All 4’s are B” or “All B’s are 4,” or it may be 
more narrowly defined as corresponding only to the case when 
both these statements were true. Complete disassociation may 
be similarly taken as corresponding to one or other of the cases. 
“No 4’s are B,” or “no o’s are 8,” or more narrowly to the 
case when both these statements are true. The greater the 
divergence of (4B) from the value (4)(B)/N towards the limit- 
ing value in either direction, the greater, we may say, is the 
intensity of association or of disassociation, so that we may speak 
of attributes being more or less, highly or slightly associated. This 
conception of degrees of association, degrees which may in fact be 
measured by certain formule (cf. § 13), is important. 
7. When the association is very slight, v.e. where (4B) only 
differs from (4)(B)/V by a few units or by a small proportion, it 
may be that such association is not really significant of any 
definite relationship. To give an illustration, suppose that a coin 
is tossed a number of times, and the tosses noted in pairs; then 
100 pairs may give such results as the following (taken from an 
actual record) :— 
First toss heads and second heads . . 26 
3) 1 » tails . 3 
First toss tails and second heads . ol 
nT tails ) 
1) 
A 
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