Hypothesis Tests for Bernoulli Experiments: Ordering the Sample Space by Bayes Factors and Using Adaptive Significance Levels for Decisions
by
Carlos A. de B. Pereira 1,*, Eduardo Y. Nakano 2, Victor Fossaluza 1, Luís Gustavo Esteves 1, Mark A. Gannon 1 and Adriano Polpo 3
Carlos A. de B. Pereira 1,*, Eduardo Y. Nakano 2, Victor Fossaluza 1, Luís Gustavo Esteves 1, Mark A. Gannon 1 and Adriano Polpo 3
1
Institute of Mathematics and Statistics, University of São Paulo, São Paulo 05508-090, Brazil
2
Department of Statistics, University of Brasília, Brasília 70910-900, Brazil
3
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)
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.
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Keywords:
significance level; sample size; Bayes factor; likelihood function; optimal decision; significance test
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MDPI and ACS Style
Pereira, C.A.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.
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