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The Stata Journal
Volume 2 Number 1: pp. 45-64

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Parameters behind “nonparametric” statistics: Kendall's tau, Somers' D and median differences

Roger Newson
King's College, London, UK
Abstract.   So-called “nonparametric” statistical methods are often in fact based on population parameters, which can be estimated (with confidence limits) using the corresponding sample statistics. This article reviews the uses of three such parameters, namely Kendall’s τα Somers’ D, and the Hodges–Lehmann median difference. Confidence intervals for these are demonstrated using the somersd package. It is argued that confidence limits for these parameters, and their differences, are more informative than the traditional practice of reporting only p-values. These three parameters are also important in defining other tests and parameters, such as the Wilcoxon test, the area under the receiver operating characteristic (ROC) curve, Harrell’s C, and the Theil median slope.
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View all articles with these keywords: confidence intervals, Gehan test, Harrell's C, Hodges–Lehmann median difference, Kendall's tau, nonparametric methods, rank correlation, rank-sum test, ROC area, Somers'~D, Theil median slope, Wilcoxon test

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