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Nonparametric Tests of Differences in Medians: Comparison of the Wilcoxon–Mann–Whitney and Robust Rank-Order Tests

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  • Nick Feltovich

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Abstract

The nonparametric Wilcoxon–Mann–Whitney test is commonly used by experimental economists for detecting differences in central tendency between two samples. This test is only theoretically appropriate under certain assumptions concerning the population distributions from which the samples are drawn, and is often used in cases where it is unclear whether these assumptions hold, and even when they clearly do not hold. Fligner and Pollicello's (1981, Journal of the American Statistical Association. 76, 162–168) robust rank-order test is a modification of the Wilcoxon–Mann–Whitney test, designed to be appropriate in more situations than Wilcoxon–Mann–Whitney. This paper uses simulations to compare the performance of the two tests under a variety of distributional assumptions. The results are mixed. The robust rank-order test tends to yield too many false positive results for medium-sized samples, but this liberalness is relatively invariant across distributional assumptions, and seems to be due to a deficiency of the normal approximation to its test statistic's distribution, rather than the test itself. The performance of the Wilcoxon–Mann–Whitney test varies hugely, depending on the distributional assumptions; in some cases, it is conservative, in others, extremely liberal. The tests have roughly similar power. Overall, the robust rank-order test performs better than Wilcoxon–Mann–Whitney, though when critical values for the robust rank-order test are not available, so that the normal approximation must be used, their relative performance depends on the underlying distributions, the sample sizes, and the level of significance used. Copyright Kluwer Academic Publishers 2003

Suggested Citation

  • Nick Feltovich, 2003. "Nonparametric Tests of Differences in Medians: Comparison of the Wilcoxon–Mann–Whitney and Robust Rank-Order Tests," Experimental Economics, Springer;Economic Science Association, vol. 6(3), pages 273-297, November.
  • Handle: RePEc:kap:expeco:v:6:y:2003:i:3:p:273-297
    DOI: 10.1023/A:1026273319211
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    References listed on IDEAS

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    1. Nick Feltovich & John Duffy, 1999. "Does observation of others affect learning in strategic environments? An experimental study," International Journal of Game Theory, Springer;Game Theory Society, vol. 28(1), pages 131-152.
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    3. Giovanna Devetag, 2000. "Coordination in "Critical Mass" Games: An Experimental Study," LEM Papers Series 2000/03, Laboratory of Economics and Management (LEM), Sant'Anna School of Advanced Studies, Pisa, Italy.
    4. Lim, Dong Hoon, 2006. "Robust edge detection in noisy images," Computational Statistics & Data Analysis, Elsevier, vol. 50(3), pages 803-812, February.
    5. Diego Aycinena & Rimvydas Baltaduonis & Lucas Rentschler, 2014. "Valuation structure in first-price and least-revenue auctions: an experimental investigation," Experimental Economics, Springer;Economic Science Association, vol. 17(1), pages 100-128, March.
    6. Duffy, John & Ochs, Jack, 2009. "Cooperative behavior and the frequency of social interaction," Games and Economic Behavior, Elsevier, vol. 66(2), pages 785-812, July.
    7. Hans-Theo Normann & Till Requate & Israel Waichman, 2014. "Do short-term laboratory experiments provide valid descriptions of long-term economic interactions? A study of Cournot markets," Experimental Economics, Springer;Economic Science Association, vol. 17(3), pages 371-390, September.
    8. Strømland, Eirik & Tjøtta, Sigve & Torsvik, Gaute, 2016. "Reciprocity evolving: partner choice and communication in a repeated prisoner’s dilemma," Working Papers in Economics 01/16, University of Bergen, Department of Economics.
    9. Francesco Feri & Bernd Irlenbusch & Matthias Sutter, 2010. "Efficiency Gains from Team-Based Coordination—Large-Scale Experimental Evidence," American Economic Review, American Economic Association, vol. 100(4), pages 1892-1912, September.
    10. Marianne LEFEBVRE & Lata GANGADHARAN & Sophie THOYER, 2011. "Do Security-differentiated Water Rights Improve Efficiency?," Working Papers 11-14, LAMETA, Universitiy of Montpellier, revised Jun 2012.
    11. Brosig-Koch, Jeannette & Helbach, Christoph & Ockenfels, Axel & Weimann, Joachim, 2011. "Still different after all these years: Solidarity behavior in East and West Germany," Journal of Public Economics, Elsevier, vol. 95(11), pages 1373-1376.
    12. Eirik Strømland & Sigve Tjøtta & Gaute Torsvik, 2016. "Cooperating, Fast and Slow: Testing the Social Heuristics Hypothesis," CESifo Working Paper Series 5875, CESifo Group Munich.
    13. Guillaume Fréchette, 2012. "Session-effects in the laboratory," Experimental Economics, Springer;Economic Science Association, vol. 15(3), pages 485-498, September.
    14. repec:eee:gamebe:v:109:y:2018:i:c:p:40-64 is not listed on IDEAS
    15. John Duffy & Dietmar Fehr, 2014. "Equilibrium Selection in Similar Repeated Games: Experimental Evidence on the Role of Precedents," Working Papers 141505, University of California-Irvine, Department of Economics.
    16. Schniter, Eric & Sheremeta, Roman & Shields, Timothy, 2015. "The Problem with All-or-nothing Trust Games: What Others Choose Not to Do Matters In Trust-based Exchange," MPRA Paper 68561, University Library of Munich, Germany.
    17. repec:pit:wpaper:274 is not listed on IDEAS
    18. Till Requate & Israel Waichman, 2011. "“A profit table or a profit calculator?” A note on the design of Cournot oligopoly experiments," Experimental Economics, Springer;Economic Science Association, vol. 14(1), pages 36-46, March.
    19. Giovanna Devetag, 2003. "Coordination and Information in Critical Mass Games: An Experimental Study," Experimental Economics, Springer;Economic Science Association, vol. 6(1), pages 53-73, June.
    20. repec:pit:wpaper:234 is not listed on IDEAS
    21. repec:eee:jeborg:v:141:y:2017:i:c:p:29-42 is not listed on IDEAS
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    23. Nadine Chlass & Jens J. Krueger, 2007. "Small Sample Properties of the Wilcoxon Signed Rank Test with Discontinuous and Dependent Observations," Jena Economic Research Papers 2007-032, Friedrich-Schiller-University Jena.
    24. Waichman, Israel & Requate, Till & Siang, Ch’ng Kean, 2014. "Communication in Cournot competition: An experimental study," Journal of Economic Psychology, Elsevier, vol. 42(C), pages 1-16.

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