{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,2,28]],"date-time":"2026-02-28T04:26:19Z","timestamp":1772252779461,"version":"3.50.1"},"reference-count":34,"publisher":"MDPI AG","issue":"12","license":[{"start":{"date-parts":[[2017,12,20]],"date-time":"2017-12-20T00:00:00Z","timestamp":1513728000000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Entropy"],"abstract":"<jats:p>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%): \u201cRaise the sample to reject the null hypothesis\u201d 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\u2013Pearson Lemma.<\/jats:p>","DOI":"10.3390\/e19120696","type":"journal-article","created":{"date-parts":[[2017,12,20]],"date-time":"2017-12-20T11:34:14Z","timestamp":1513769654000},"page":"696","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":8,"title":["Hypothesis Tests for Bernoulli Experiments: Ordering the Sample Space by Bayes Factors and Using Adaptive Significance Levels for Decisions"],"prefix":"10.3390","volume":"19","author":[{"ORCID":"https:\/\/orcid.org\/0000-0001-6315-7484","authenticated-orcid":false,"given":"Carlos","family":"Pereira","sequence":"first","affiliation":[{"name":"Institute of Mathematics and Statistics, University of S\u00e3o Paulo, S\u00e3o Paulo 05508-090, Brazil"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-9071-8512","authenticated-orcid":false,"given":"Eduardo","family":"Nakano","sequence":"additional","affiliation":[{"name":"Department of Statistics, University of Bras\u00edlia, Bras\u00edlia 70910-900, Brazil"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Victor","family":"Fossaluza","sequence":"additional","affiliation":[{"name":"Institute of Mathematics and Statistics, University of S\u00e3o Paulo, S\u00e3o Paulo 05508-090, Brazil"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Lu\u00eds","family":"Esteves","sequence":"additional","affiliation":[{"name":"Institute of Mathematics and Statistics, University of S\u00e3o Paulo, S\u00e3o Paulo 05508-090, Brazil"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Mark","family":"Gannon","sequence":"additional","affiliation":[{"name":"Institute of Mathematics and Statistics, University of S\u00e3o Paulo, S\u00e3o Paulo 05508-090, Brazil"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Adriano","family":"Polpo","sequence":"additional","affiliation":[{"name":"Department of Statistics, Federal University of S\u00e3o Carlos, S\u00e3o Carlos 13565-905, Brazil"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"1968","published-online":{"date-parts":[[2017,12,20]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","first-page":"19313","DOI":"10.1073\/pnas.1313476110","article-title":"Revised standards for statistical evidence","volume":"110","author":"Johnson","year":"2013","journal-title":"Proc. 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