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In statistics, the Kendall rank correlation coefficient, commonly referred to as Kendall's tau coefficient (after the Greek letter τ), is a statistic used to measure the association between two measured quantities. A tau test is a non-parametric hypothesis test for statistical dependence based on the tau coefficient. It is a measure of rank correlation: the similarity of the orderings of the data when ranked by each of the quantities. It is named after Maurice Kendall, who developed it in 1938, though Gustav Fechner had proposed a similar measure in the context of time series in 1897. ==Definition== Let (''x''1, ''y''1), (''x''2, ''y''2), …, (''x''''n'', ''y''''n'') be a set of observations of the joint random variables ''X'' and ''Y'' respectively, such that all the values of (''x''''i'') and (''y''''i'') are unique. Any pair of observations (''x''''i'', ''y''''i'') and (''x''''j'', ''y''''j'') are said to be ''concordant'' if the ranks for both elements agree: that is, if both ''x''''i'' > ''x''''j'' and ''y''''i'' > ''y''''j'' or if both ''x''''i'' < ''x''''j'' and ''y''''i'' < ''y''''j''. They are said to be ''discordant'', if ''x''''i'' > ''x''''j'' and ''y''''i'' < ''y''''j'' or if ''x''''i'' < ''x''''j'' and y''i'' > ''y''''j''. If ''x''''i'' = ''x''''j'' or ''y''''i'' = ''y''''j'', the pair is neither concordant nor discordant. The Kendall τ coefficient is defined as: : 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「Kendall rank correlation coefficient」の詳細全文を読む スポンサード リンク
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