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

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  • Roger Newson

    () (King's College, London)

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 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.

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  • 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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    1. 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.
    2. Nicholas J. Cox, 2001. "Speaking Stata: How to repeat yourself without going mad," Stata Journal, StataCorp LP, vol. 1(1), pages 86-97, November.
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    Cited by:

    1. Dirk Tasche, 2009. "Estimating discriminatory power and PD curves when the number of defaults is small," Papers 0905.3928, arXiv.org, revised Mar 2010.
    2. Nicholas J. Cox, 2002. "Speaking Stata: How to face lists with fortitude," Stata Journal, StataCorp LP, vol. 2(2), pages 202-222, May.
    3. Newson, Roger, 2005. "Efficient Calculation of Jackknife Confidence Intervals for Rank Statistics," Journal of Statistical Software, Foundation for Open Access Statistics, vol. 15(i01).
    4. 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.
    5. 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.
    6. 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.
    7. 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.
    8. 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.
    9. 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.
    10. 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.
    11. 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.
    12. Peter, Eckley, 2015. "Measuring economic uncertainty using news-media textual data," MPRA Paper 64874, University Library of Munich, Germany, revised 01 May 2015.
    13. Roger B. Newson, 2010. "Comparing the predictive powers of survival models using Harrell’s C or Somers’ D," Stata Journal, StataCorp LP, vol. 10(3), pages 339-358, September.
    14. Chakrabarty, Manisha & Hildenbrand, Werner, 2011. "Engel's Law Reconsidered," Journal of Mathematical Economics, Elsevier, vol. 47(3), pages 289-299.
    15. 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.
    16. 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.
    17. Manisha Chakrabarty & Werner Hildenbrand, 2009. "Engel’s Law Reconsidered," Bonn Econ Discussion Papers bgse22_2009, University of Bonn, Germany.
    18. 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.
    19. 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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