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