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In statistics, and especially in biostatistics, cophenetic correlation〔Sokal, R. R. and F. J. Rohlf. 1962. The comparison of dendrograms by objective methods. Taxon, 11:33-40〕 (more precisely, the cophenetic correlation coefficient) is a measure of how faithfully a dendrogram preserves the pairwise distances between the original unmodeled data points. Although it has been most widely applied in the field of biostatistics (typically to assess cluster-based models of DNA sequences, or other taxonomic models), it can also be used in other fields of inquiry where raw data tend to occur in clumps, or clusters.〔Dorthe B. Carr, Chris J. Young, Richard C. Aster, and Xioabing Zhang, (''Cluster Analysis for CTBT Seismic Event Monitoring'' ) (a study prepared for the U.S. Department of Energy)〕 This coefficient has also been proposed for use as a test for nested clusters.〔Rohlf, F. J. and David L. Fisher. 1968. Test for hierarchical structure in random data sets. Systematic Zool., 17:407-412〕 ==Calculating the cophenetic correlation coefficient== Suppose that the original data have been modeled using a cluster method to produce a dendrogram ; that is, a simplified model in which data that are "close" have been grouped into a hierarchical tree. Define the following distance measures. *''x''(''i'', ''j'') = | ''Xi'' − ''Xj'' |, the ordinary Euclidean distance between the ''i''th and ''j''th observations. *''t''(''i'', ''j'') = the dendrogrammatic distance between the model points ''Ti'' and ''Tj''. This distance is the height of the node at which these two points are first joined together. Then, letting be the average of the ''x''(''i'', ''j''), and letting be the average of the ''t''(''i'', ''j''), the cophenetic correlation coefficient ''c'' is given by〔(Mathworks statistics toolbox )〕 : 抄文引用元・出典: フリー百科事典『 ウィキペディア（Wikipedia）』 ■ウィキペディアで「Cophenetic correlation」の詳細全文を読む スポンサード リンク
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