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

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

Research output: Contribution to journalArticle

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.

Original languageEnglish
Article number696
Number of pages15
JournalEntropy
Volume19
Issue number12
DOIs
Publication statusPublished - Dec 2017
Externally publishedYes

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