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Congruence coefficient : ウィキペディア英語版 | Congruence coefficient In multivariate statistics, the congruence coefficient is an index of the similarity between factors that have been derived in a factor analysis. It was introduced in 1948 by Cyril Burt who referred to it as ''unadjusted correlation''. It is also called ''Tucker's congruence coefficient'' after Ledyard Tucker who popularized the technique. Its values range between -1 and +1. It can be used to study the similarity of extracted factors across different samples of, for example, test takers who have taken the same test.〔Lorenzo-Seva, U. & ten Berge, J.M.F. (2006). Tucker’s Congruence Coefficient as a Meaningful Index of Factor Similarity. ''Methodology, 2,'' 57–64.〕〔Jensen, A.R. (1998). ''The ''g'' factor: The science of mental ability''. Westport, CT: Praeger, pp. 99–100.〕〔Abdi, H. (2007). (RV Coefficient and Congruence Coefficient. ) In Neil Salkind (Ed.), ''Encyclopedia of Measurement and Statistics.'' Thousand Oaks (CA): Sage.〕 ==Definition==
Let ''X'' and ''Y'' be column vectors of factor loadings for two different samples. The formula for the congruence coefficient, or ''rc'', is then〔 :
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