Parameters behind “Nonparametric” Statistics: Kendall's tau, Somers’ D and Median Differences
- 1 January 2002
- journal article
- research article
- Published by SAGE Publications in The Stata Journal: Promoting communications on statistics and Stata
- Vol. 2 (1), 45-64
- https://doi.org/10.1177/1536867x0200200103
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 τa, 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.Keywords
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