Hypothesis Tests for Bernoulli Experiments: Ordering the Sample Space by Bayes Factors and Using Adaptive Significance Levels for Decisions

Pereira, Carlos A. de B.; Nakano, Eduardo Y.; Fossaluza, Victor; Esteves, Luís Gustavo; Gannon, Mark A.; Polpo, Adriano

doi:10.3390/e19120696

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Hypothesis Tests for Bernoulli Experiments: Ordering the Sample Space by Bayes Factors and Using Adaptive Significance Levels for Decisions

Carlos A. de B. Pereira

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Institute of Mathematics and Statistics, University of São Paulo, São Paulo 05508-090, Brazil

Department of Statistics, University of Brasília, Brasília 70910-900, Brazil

Department of Statistics, Federal University of São Carlos, São Carlos 13565-905, Brazil

Author to whom correspondence should be addressed.

Entropy 2017, 19(12), 696; https://doi.org/10.3390/e19120696

Received: 31 August 2017 / Revised: 18 December 2017 / Accepted: 18 December 2017 / Published: 20 December 2017

(This article belongs to the Special Issue Maximum Entropy and Bayesian Methods)

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Abstract

The main objective of this paper is to find the relation between the adaptive significance level presented here and the sample size. We statisticians know of the inconsistency, or paradox, in the current classical tests of significance that are based on p-value statistics that are compared to the canonical significance levels (10%, 5%, and 1%): “Raise the sample to reject the null hypothesis” is the recommendation of some ill-advised scientists! This paper will show that it is possible to eliminate this problem of significance tests. We present here the beginning of a larger research project. The intention is to extend its use to more complex applications such as survival analysis, reliability tests, and other areas. The main tools used here are the Bayes factor and the extended Neyman–Pearson Lemma. View Full-Text

Keywords: significance level; sample size; Bayes factor; likelihood function; optimal decision; significance test

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Pereira, C.A.d.B.; Nakano, E.Y.; Fossaluza, V.; Esteves, L.G.; Gannon, M.A.; Polpo, A. Hypothesis Tests for Bernoulli Experiments: Ordering the Sample Space by Bayes Factors and Using Adaptive Significance Levels for Decisions. Entropy 2017, 19, 696. https://doi.org/10.3390/e19120696

AMA Style

Pereira CAdB, Nakano EY, Fossaluza V, Esteves LG, Gannon MA, Polpo A. Hypothesis Tests for Bernoulli Experiments: Ordering the Sample Space by Bayes Factors and Using Adaptive Significance Levels for Decisions. Entropy. 2017; 19(12):696. https://doi.org/10.3390/e19120696

Chicago/Turabian Style

Pereira, Carlos A.d.B., Eduardo Y. Nakano, Victor Fossaluza, Luís G. Esteves, Mark A. Gannon, and Adriano Polpo. 2017. "Hypothesis Tests for Bernoulli Experiments: Ordering the Sample Space by Bayes Factors and Using Adaptive Significance Levels for Decisions" Entropy 19, no. 12: 696. https://doi.org/10.3390/e19120696

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Hypothesis Tests for Bernoulli Experiments: Ordering the Sample Space by Bayes Factors and Using Adaptive Significance Levels for Decisions

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