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


  • Roger Newson

    () (King's College, London)


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 tau, 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. Copyright 2002 by Stata Corporation.

Suggested Citation

  • Roger Newson, 2002. "Parameters behind "nonparametric" statistics: Kendall's tau,Somers' D and median differences," Stata Journal, StataCorp LP, vol. 2(1), pages 45-64, February.
  • Handle: RePEc:tsj:stataj:v:2:y:2002:i:1:p:45-64

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    5. Bateman, Ian J. & Brouwer, Roy, 2006. "Consistency and construction in stated WTP for health risk reductions: A novel scope-sensitivity test," Resource and Energy Economics, Elsevier, vol. 28(3), pages 199-214, August.
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    8. Regier, Dean A. & Bentley, Colene & Mitton, Craig & Bryan, Stirling & Burgess, Michael M. & Chesney, Ellen & Coldman, Andy & Gibson, Jennifer & Hoch, Jeffrey & Rahman, Syed & Sabharwal, Mona & Sawka, , 2014. "Public engagement in priority-setting: Results from a pan-Canadian survey of decision-makers in cancer control," Social Science & Medicine, Elsevier, vol. 122(C), pages 130-139.
    9. Lukasz Prorokowski, 2016. "Rank-order statistics for validating discriminative power of credit risk models," Bank i Kredyt, Narodowy Bank Polski, vol. 47(3), pages 227-250.
    10. Johannes Kaiser & Michael G. Lacy, 2009. "A general-purpose method for two-group randomization tests," Stata Journal, StataCorp LP, vol. 9(1), pages 70-85, March.
    11. John, Katrin & Thomsen, Stephan L., 2015. "School-track environment or endowment: What determines different other-regarding behavior across peer groups?," Games and Economic Behavior, Elsevier, vol. 94(C), pages 122-141.
    12. Hanna Karolina Szymborska, 2018. "Household wealth structures and position in the income distribution – econometric analysis for the USA, 1989-2013," Working Papers PKWP1806, Post Keynesian Economics Society (PKES).
    13. Tomas Miklanek, 2017. "The Effect of Shame in Dictator Games with Information Asymmetry," CERGE-EI Working Papers wp581, The Center for Economic Research and Graduate Education - Economics Institute, Prague.
    14. Löschel, Andreas & Sturm, Bodo & Uehleke, Reinhard, 2013. "Revealed preferences for climate protection when the purely individual perspective is relaxed: Evidence from a framed field experiment," ZEW Discussion Papers 13-006, ZEW - Zentrum für Europäische Wirtschaftsforschung / Center for European Economic Research.
    15. Tosun, Jale, 2012. "Emergency oil stocks in Southeastern and Eastern Europe: What explains variation in convergence towards the EU model?," Energy Policy, Elsevier, vol. 46(C), pages 417-426.
    16. Peter, Eckley, 2015. "Measuring economic uncertainty using news-media textual data," MPRA Paper 64874, University Library of Munich, Germany, revised 01 May 2015.
    17. Newson, Roger B., 2010. "Comparing the predictive powers of survival models using Harrell's C or Somers' D," Stata Journal, StataCorp LP, vol. 0(Number 3), pages 1-20.
    18. Chakrabarty, Manisha & Hildenbrand, Werner, 2011. "Engel's Law Reconsidered," Journal of Mathematical Economics, Elsevier, vol. 47(3), pages 289-299.
    19. Ramos, Héctor M. & Ollero, Jorge & Suárez-Llorens, Alfonso, 2017. "A new explanatory index for evaluating the binary logistic regression based on the sensitivity of the estimated model," Statistics & Probability Letters, Elsevier, vol. 120(C), pages 135-140.
    20. Nazim, Habibov & Elvin, Afandi, 2009. "Analysis of subjective wellbeing in low-income transitional countries: evidence from comparative national surveys in Armenia,Azerbaijan and Georgia," MPRA Paper 42720, University Library of Munich, Germany.
    21. Löschel, Andreas & Sturm, Bodo & Uehleke, Reinhard, 2017. "Revealed preferences for voluntary climate change mitigation when the purely individual perspective is relaxed – evidence from a framed field experiment," Journal of Behavioral and Experimental Economics (formerly The Journal of Socio-Economics), Elsevier, vol. 67(C), pages 149-160.
    22. Roger Newson, 2006. "On the central role of Somers' D," United Kingdom Stata Users' Group Meetings 2006 01, Stata Users Group.


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