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翻訳と辞書　辞書検索 [ 開発暫定版 ] スポンサード リンク Kendall's W ： ウィキペディア英語版 Kendall's W Kendall's ''W'' (also known as Kendall's coefficient of concordance) is a non-parametric statistic. It is a normalization of the statistic of the Friedman test, and can be used for assessing agreement among raters. Kendall's ''W'' ranges from 0 (no agreement) to 1 (complete agreement). Suppose, for instance, that a number of people have been asked to rank a list of political concerns, from most important to least important. Kendall's ''W'' can be calculated from these data. If the test statistic ''W'' is 1, then all the survey respondents have been unanimous, and each respondent has assigned the same order to the list of concerns. If ''W'' is 0, then there is no overall trend of agreement among the respondents, and their responses may be regarded as essentially random. Intermediate values of ''W'' indicate a greater or lesser degree of unanimity among the various responses. While tests using the standard Pearson correlation coefficient assume normally distributed values and compare two sequences of outcomes at a time, Kendall's ''W'' makes no assumptions regarding the nature of the probability distribution and can handle any number of distinct outcomes. ''W'' is linearly related to the mean value of the Spearman's rank correlation coefficients between all pairs of the rankings over which it is calculated. ==Definition== Suppose that object ''i'' is given the rank ''ri,j'' by judge number ''j'', where there are in total ''n'' objects and ''m'' judges. Then the total rank given to object ''i'' is :$R\_i=\backslash sum\_^m\; r\_\; ,$ and the mean value of these total ranks is :$\backslash bar\; R=\; \backslash frac\; \backslash sum\_^n\; R\_i.$ The sum of squared deviations, ''S'', is defined as :$S=\backslash sum\_^n\; (R\_i-\; \backslash bar\; R)^2\; ,$ and then Kendall's ''W'' is defined as〔Dodge (2003): see "concordance, coefficient of"〕 :$W=\backslash frac.$ If the test statistic ''W'' is 1, then all the judges or survey respondents have been unanimous, and each judge or respondent has assigned the same order to the list of objects or concerns. If ''W'' is 0, then there is no overall trend of agreement among the respondents, and their responses may be regarded as essentially random. Intermediate values of ''W'' indicate a greater or lesser degree of unanimity among the various judges or respondents. Legendre〔Legendre (2005)〕 discusses a variant of the ''W'' statistic which accommodates ties in the rankings and also describes methods of making significance tests based on ''W''. 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's W」の詳細全文を読む スポンサード リンク 翻訳と辞書 : 翻訳のためのインターネットリソース Copyright(C) kotoba.ne.jp 1997-2016. All Rights Reserved.