An Introduction to the theory of statistics

Bibliographic data

Monograph

Identifikator:: 1751730271

URN:: urn:nbn:de:zbw-retromon-127610

Document type:: Monograph

Author:: Yule, George Udny http://d-nb.info/gnd/12910504X

Title:: An Introduction to the theory of statistics

Edition:: 8. ed. rev

Place of publication:: London

Publisher:: Griffin

Year of publication:: 1927

Scope:: XV, 422 S; Ill., Diagr

Digitisation:: 2021

Collection:: Economics Books

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Chapter

Document type:: Monograph

Structure type:: Chapter

Title:: Part I. The theory of atributes

Collection:: Economics Books

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 " 1"

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