Preprint Article Version 1 This version is not peer-reviewed

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

Version 1 : Received: 23 September 2017 / Approved: 25 September 2017 / Online: 25 September 2017 (08:33:18 CEST)

A peer-reviewed article of this Preprint also exists.

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. 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.

Journal reference: Entropy 2017, 19, 696
DOI: 10.3390/e19120696

Abstract

The main objective of this paper is to find a close link between the adaptive level of significance, 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 is 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. The Bayesian Lindley's paradox – "increase the sample to accept the hypothesis" – also disappears. Obviously, we present here only the beginning of a possible prominent research. 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.

Subject Areas

significance level; sample size; bayes ratio; likelihood function; optimal decision; significance test

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