An Introduction to the theory of statistics

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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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IV.—PARTIAL ASSOCIATION. The two data give— a (AC)(BC : (4BC) = Ms | | ) (45) — AVE) Id) = (CB) ~ (BOY) (¥) ¥) Adding them together we have— (45)= ri | MACY BC) - (A)(C)BO) ~ (BXCNAC) +(A)BXO) } Write, as in § 11 of Chap. ITI. (p. 35)— (4)(B) A)(c (B)(C) (48), = NB) (40), NO) (py, BNO) subtract (45), from both sides of the above equation, simplify, and we have N (4B) ~ (4B)y = ((5[(AC) ~ (4C)IBO) - (BOY) (4) This proves the theorem; for the right-hand side will not be zero unless either (AC) =(4C), or (BC) = (£C),. 7. The result indicates that, while no degree of heterogeneity in the universe can influence the association between 4 and B if all other attributes are independent of either 4 or 7B or both, an illusory or misleading association may arise in any case where there exists in the given universe a third attribute C' with which both 4 and B are associated (positively or negatively). If both associations are of the same sign, the resulting illusory association between 4 and B will be positive ; if of opposite sign, negative. The three illustrations of § 2 are all of the first kind. In (1) it is argued that the positive associations between vaccination and hygienic conditions, exemption from attack and hygienic conditions, give rise to an illusory positive association between vaccination and exemption from attack. In (2) it is argued that the positive associations between conservative and winning, conservative and spending more, give rise to an illusory positive association between winning and spending more. In (3) the question is raised whether the positive association between grandparent and grandchild may not be due solely to the positive associations between grandparent and parent, parent and child. Misleading associations of this kind may easily arise through a4 49 (3

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