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.

De Capitani, L., & De Martini, D. (2016). Reproducibility probability estimation and RP-testing for some nonparametric tests. ENTROPY, 18(4) [10.3390/e18040142].

Reproducibility probability estimation and RP-testing for some nonparametric tests

De Capitani, L;De Martini, D
2016

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.
Articolo in rivista - Articolo scientifico
Scientifica
Asymptotic power approximation; Binomial test; Kendall test; Reproducibility of tests outcomes; Sign test; Stability of test outcomes; Wilcoxon signed rank test;
Asymptotic power approximation; Binomial test; Kendall test; Reproducibility of tests outcomes; Sign test; Stability of test outcomes; Wilcoxon signed rank test; Physics and Astronomy (all)
English
De Capitani, L., & De Martini, D. (2016). Reproducibility probability estimation and RP-testing for some nonparametric tests. ENTROPY, 18(4) [10.3390/e18040142].
De Capitani, L; De Martini, D
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Utilizza questo identificativo per citare o creare un link a questo documento: http://hdl.handle.net/10281/191665
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