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A new method for constructing exact tests without making any assumptions

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  • Karl Schlag

Abstract

We present a new method for constructing exact distribution-free tests (and confidence intervals) for variables that can generate more than two possible outcomes. This method separates the search for an exact test from the goal to create a non- randomized test. Randomization is used to extend any exact test relating to means of variables with finitely many outcomes to variables with outcomes belonging to a given bounded set. Tests in terms of variance and covariance are reduced to tests relating to means. Randomness is then eliminated in a separate step. This method is used to create confidence intervals for the difference between two means (or variances) and tests of stochastic inequality and correlation.

Suggested Citation

  • Karl Schlag, 2008. "A new method for constructing exact tests without making any assumptions," Economics Working Papers 1109, Department of Economics and Business, Universitat Pompeu Fabra.
    • Handle: RePEc:upf:upfgen:1109
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    References listed on IDEAS

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    1. Fishman, George S., 1991. "Confidence intervals for the mean in the bounded case," Statistics & Probability Letters, Elsevier, vol. 12(3), pages 223-227, September.
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    3. Nancy Buchan & Rachel Croson, 1999. "Gender and Culture: International Experimental Evidence from Trust Games," American Economic Review, American Economic Association, vol. 89(2), pages 386-391, May.
    4. Djankov, Simeon & La Porta, Rafael & Lopez-de-Silanes, Florencio & Shleifer, Andrei, 2008. "The law and economics of self-dealing," Journal of Financial Economics, Elsevier, vol. 88(3), pages 430-465, June.
    5. Romano, Joseph P. & Wolf, Michael, 2001. "Explicit nonparametric confidence intervals for the variance with guaranteed coverage," DES - Working Papers. Statistics and Econometrics. WS ws010302, Universidad Carlos III de Madrid. Departamento de Estadística.
    6. Karl Schlag, 2008. "Bringing game theory to hypothesis testing: Establishing finite sample bounds on inference," Economics Working Papers 1099, Department of Economics and Business, Universitat Pompeu Fabra.
    7. Africa Borges del Rosal & Concepción San Luis & Alfonso Sánchez-Bruno, 2003. "Dominance Statistics: A Simulation Study on the d Statistic," Quality & Quantity: International Journal of Methodology, Springer, vol. 37(3), pages 303-316, August.
    8. Reiczigel, Jeno & Zakarias, Ildiko & Rozsa, Lajos, 2005. "A Bootstrap Test of Stochastic Equality of Two Populations," The American Statistician, American Statistical Association, vol. 59, pages 156-161, May.
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    Citations

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    Cited by:

    1. Galbiati, Roberto & Schlag, Karl H. & van der Weele, Joël J., 2013. "Sanctions that signal: An experiment," Journal of Economic Behavior & Organization, Elsevier, vol. 94(C), pages 34-51.
    2. Bernhard Kasberger & Karl H. Schlag, 2017. "Robust Bidding in First-Price Auctions: How to Bid without Knowing what Otheres are Doing," Vienna Economics Papers 1707, University of Vienna, Department of Economics.
    3. Karl H.Schlag, 2015. "Who gives Direction to Statistical Testing? Best Practice meets Mathematically Correct Tests," Vienna Economics Papers vie1512, University of Vienna, Department of Economics.
    4. Bernhard Kasberger & Karl H. Schlag, 2017. "Robust Bidding in First-Price Auctions: How to Bid without Knowing what Otheres are Doing," Vienna Economics Papers vie1707, University of Vienna, Department of Economics.
    5. Heczko, Alexander & Kittsteiner, Thomas & Ott, Marion, 2023. "The benefits of auctioneer competition: Merging auctions and adding auctioneers," ZEW Discussion Papers 23-038, ZEW - Leibniz Centre for European Economic Research.
    6. Matteo Rizzolli & James Tremewan, 2016. "Hard Labour in the lab: Are monetary and non-monetary sanctions really substitutable?," Vienna Economics Papers vie1606, University of Vienna, Department of Economics.
    7. Lippert, Steffen & Tremewan, James, 2021. "Pledge-and-review in the laboratory," Games and Economic Behavior, Elsevier, vol. 130(C), pages 179-195.
    8. Karl Schlag & James Tremewan, 2021. "Simple belief elicitation: An experimental evaluation," Journal of Risk and Uncertainty, Springer, vol. 62(2), pages 137-155, April.
    9. Heczko, Alexander & Kittsteiner, Thomas & Ott, Marion, 2018. "The Performance of Core-Selecting Auctions: An Experiment," EconStor Preprints 176842, ZBW - Leibniz Information Centre for Economics.
    10. Dugar, Subhasish & Mitra, Arnab & Shahriar, Quazi, 2019. "Deception: The role of uncertain consequences," European Economic Review, Elsevier, vol. 114(C), pages 1-18.
    11. Thomas A. Stephens & Jean-Robert Tyran, 2012. "“At least I didn’t lose money” - Nominal Loss Aversion Shapes Evaluations of Housing Transactions," Discussion Papers 12-14, University of Copenhagen. Department of Economics.
    12. Gossner, Olivier & Schlag, Karl H., 2013. "Finite-sample exact tests for linear regressions with bounded dependent variables," Journal of Econometrics, Elsevier, vol. 177(1), pages 75-84.
    13. Karl H.Schlag, 2015. "Who gives Direction to Statistical Testing? Best Practice meets Mathematically Correct Tests," Vienna Economics Papers 1512, University of Vienna, Department of Economics.
    14. Müller, Julia & Schwieren, Christiane & Spitzer, Florian, 2022. "How to prevent destruction – On the malleability of anti-social behavior," Journal of Behavioral and Experimental Economics (formerly The Journal of Socio-Economics), Elsevier, vol. 97(C).
    15. Galbiati, Roberto & Schlag, Karl H. & van der Weele, Joël J., 2013. "Sanctions that signal: An experiment," Journal of Economic Behavior & Organization, Elsevier, vol. 94(C), pages 34-51.
    16. repec:hal:spmain:info:hdl:2441/7o52iohb7k6srk09o0ks2e12i is not listed on IDEAS
    17. Chakrabarty, Manisha & Hildenbrand, Werner, 2011. "Engel's Law Reconsidered," Journal of Mathematical Economics, Elsevier, vol. 47(3), pages 289-299.
    18. Roberto Galbiati & Karl Schlag & Joël van der Weele, 2009. "Can sanctions induce pessimism? An experiment," Economics Working Papers 1150, Department of Economics and Business, Universitat Pompeu Fabra.
    19. Müller, Julia & Schwieren, Christiane & Spitzer, Florian, 2016. "What Drives Destruction? On the Malleability of Anti-Social Behavior," Department of Economics Working Paper Series 238, WU Vienna University of Economics and Business.
    20. Matteo Rizzolli & James Tremewan, 2016. "Hard Labour in the lab: Are monetary and non-monetary sanctions really substitutable?," Vienna Economics Papers 1606, University of Vienna, Department of Economics.
    21. Karl Schlag & Olivier Gossner, 2010. "Finite sample nonparametric tests for linear regressions," Economics Working Papers 1212, Department of Economics and Business, Universitat Pompeu Fabra.

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    More about this item

    Keywords

    Distribution-free; nonparametric; exact hypothesis testing; unavoidable inaccuracy; nonparametric Behrens-Fisher problem; UMPU test; Kendall's tau; Qn;
    All these keywords.

    JEL classification:

    • C12 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Hypothesis Testing: General
    • C14 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Semiparametric and Nonparametric Methods: General

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