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kendall's w

Kendall's W (also known as Kendall's coefficient of concordance) is a non-parametric statistic for rank correlation. It is a normalization of the statistic of the Friedman test, and can be used for assessing agreement among raters and in particular inter-rater reliability. 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 the most important to the 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 simultaneously, Kendall's W makes no assumptions regarding the nature of the probability distribution and can handle any number of distinct outcomes.

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