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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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    File URL: https://econ-papers.upf.edu/papers/1109.pdf
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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.
    2. Quinn McNemar, 1947. "Note on the sampling error of the difference between correlated proportions or percentages," Psychometrika, Springer;The Psychometric Society, vol. 12(2), pages 153-157, June.
    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. 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.
    3. 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.
    4. 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.
    5. Chakrabarty, Manisha & Hildenbrand, Werner, 2011. "Engel's Law Reconsidered," Journal of Mathematical Economics, Elsevier, vol. 47(3), pages 289-299.
    6. 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.
    7. Müller, Julia & Schwieren, Christiane & Spitzer, Florian, 2016. "What Drives Destruction? On the Malleability of Anti-Social Behavior," Department of Economics Working Paper Series 5343, WU Vienna University of Economics and Business.
    8. Karl Schlag & Olivier Gossner, 2010. "Finite sample nonparametric tests for linear regressions," Economics Working Papers 1212, Department of Economics and Business, Universitat Pompeu Fabra.

    More about this item

    Keywords

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

    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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