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Association (statistics) : ウィキペディア英語版 | Association (statistics) In statistics, an association is any relationship between two measured quantities that renders them statistically dependent.〔Upton, G., Cook, I. (2006) ''Oxford Dictionary of Statistics'', 2nd Edition, OUP. ISBN 978-0-19-954145-4〕 The term "association" is closely related to the term "correlation." Both terms imply that two or more variables vary according to some pattern. However, correlation is more rigidly defined by some correlation coefficient which measures the degree to which the association of the variables tends to a certain pattern. Sometimes the pattern of association is a simple linear relationship (as in the case of the popular Pearson product moment correlation coefficient (commonly called simply "the correlation coefficient"), although other forms of correlation are better suited to non-linear associations.〔Croxton, Frederick Emory; Cowden, Dudley Johnstone; Klein, Sidney (1968) ''Applied General Statistics'', Pitman. ISBN 9780273403159 (page 625)〕〔Dietrich, Cornelius Frank (1991) ''Uncertainty, Calibration and Probability: The Statistics of Scientific and Industrial Measurement'' 2nd Edition, A. Higler. ISBN 9780750300605 (Page 331)〕〔Aitken, Alexander Craig (1957) ''Statistical Mathematics'' 8th Edition. Oliver & Boyd. ISBN 9780050013007 (Page 95)〕 ==Measures of association== There are many statistical measures of association that can be used to infer the presence or absence of association in a sample of data. Examples of such measures of association include the Pearson product moment correlation coefficient (mentioned above), the odds ratio "OR," Risk Ratio "RR," Absolute Risk Reduction "ARR" (all three of which ratios are used for dichotomous measurements), as well as other measures of association such as distance correlation, tetrachoric correlation coefficient, Goodman and Kruskal's lambda, Tschuprow's T and Cramér's V, or in information theory measures such as mutual information.
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