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On stochastic orderings of the Wilcoxon Rank Sum test statistic--With applications to reproducibility probability estimation testing

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  • De Capitani, L.
  • De Martini, D.

Abstract

Recently, the possibility of testing statistical hypotheses through the estimate of the reproducibility probability (i.e. the estimate of the power of the statistical test) in a general parametric framework has been introduced. In this paper, we provide some results on the stochastic orderings of the Wilcoxon Rank Sum (WRS) statistic, implying, for example, that the related test is strictly unbiased. Moreover, under some regularity conditions, we show that it is possible to define a continuous and strictly monotone power function of the WRS test. This last result is useful in order to obtain a point estimator and lower bounds for the power of the WRS test. In analogy with the parametric setting, we show that these power estimators, alias reproducibility probability estimators, can be used as test statistic, i.e. it is possible to refer directly to the estimate of the reproducibility probability to perform the WRS test. Some reproducibility probability estimators based on asymptotic approximations of the power are provided. A brief simulation shows a very high agreement between the approximated reproducibility probability based tests and the classical one.

Suggested Citation

  • De Capitani, L. & De Martini, D., 2011. "On stochastic orderings of the Wilcoxon Rank Sum test statistic--With applications to reproducibility probability estimation testing," Statistics & Probability Letters, Elsevier, vol. 81(8), pages 937-946, August.
    • Handle: RePEc:eee:stapro:v:81:y:2011:i:8:p:937-946
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    References listed on IDEAS

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    1. B. Rosner & R. J. Glynn, 2009. "Power and Sample Size Estimation for the Wilcoxon Rank Sum Test with Application to Comparisons of C Statistics from Alternative Prediction Models," Biometrics, The International Biometric Society, vol. 65(1), pages 188-197, March.
    2. De Martini, Daniele, 2008. "Reproducibility probability estimation for testing statistical hypotheses," Statistics & Probability Letters, Elsevier, vol. 78(9), pages 1056-1061, July.
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    Cited by:

    1. Bagnato, Luca & De Capitani, Lucio & Mazza, Angelo & Punzo, Antonio, 2015. "SDD: An R Package for Serial Dependence Diagrams," Journal of Statistical Software, Foundation for Open Access Statistics, vol. 64(c02).
    2. Luca Bagnato & Lucio De Capitani & Antonio Punzo, 2014. "Detecting serial dependencies with the reproducibility probability autodependogram," AStA Advances in Statistical Analysis, Springer;German Statistical Society, vol. 98(1), pages 35-61, January.
    3. Lucio De Capitani & Daniele De Martini, 2021. "Improving reproducibility probability estimation and preserving RP-testing," Statistical Methods & Applications, Springer;Società Italiana di Statistica, vol. 30(1), pages 49-77, March.
    4. Luca Bagnato & Lucio De Capitani & Antonio Punzo, 2017. "A diagram to detect serial dependencies: an application to transport time series," Quality & Quantity: International Journal of Methodology, Springer, vol. 51(2), pages 581-594, March.

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