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Entropy 2016, 18(4), 142; doi:10.3390/e18040142

Reproducibility Probability Estimation and RP-Testing for Some Nonparametric Tests

Department of Statistics and Quantitative Methods, University of Milano-Bicocca, via Bicocca degli Arcimboldi, 8, Milano 20126, Italy
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Academic Editors: Julio Stern, Adriano Polpo and Kevin H. Knuth
Received: 13 January 2016 / Revised: 10 March 2016 / Accepted: 6 April 2016 / Published: 16 April 2016
(This article belongs to the Special Issue Statistical Significance and the Logic of Hypothesis Testing)
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Abstract

Several reproducibility probability (RP)-estimators for the binomial, sign, Wilcoxon signed rank and Kendall tests are studied. Their behavior in terms of MSE is investigated, as well as their performances for RP-testing. Two classes of estimators are considered: the semi-parametric one, where RP-estimators are derived from the expression of the exact or approximated power function, and the non-parametric one, whose RP-estimators are obtained on the basis of the nonparametric plug-in principle. In order to evaluate the precision of RP-estimators for each test, the MSE is computed, and the best overall estimator turns out to belong to the semi-parametric class. Then, in order to evaluate the RP-testing performances provided by RP estimators for each test, the disagreement between the RP-testing decision rule, i.e., “accept H0 if the RP-estimate is lower than, or equal to, 1/2, and reject H0 otherwise”, and the classical one (based on the critical value or on the p-value) is obtained. It is shown that the RP-based testing decision for some semi-parametric RP estimators exactly replicates the classical one. In many situations, the RP-estimator replicating the classical decision rule also provides the best MSE. View Full-Text
Keywords: asymptotic power approximation; sign test; binomial test; Wilcoxon signed rank test; Kendall test; stability of test outcomes; reproducibility of tests outcomes asymptotic power approximation; sign test; binomial test; Wilcoxon signed rank test; Kendall test; stability of test outcomes; reproducibility of tests outcomes
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This is an open access article distributed under the Creative Commons Attribution License which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited. (CC BY 4.0).

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MDPI and ACS Style

De Capitani, L.; De Martini, D. Reproducibility Probability Estimation and RP-Testing for Some Nonparametric Tests. Entropy 2016, 18, 142.

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