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

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

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.

EXPERIMENTAL design; MATHEMATICAL optimization; ECONOMETRIC models; MULTILEVEL models; STATISTICAL hypothesis testing

Entropy, 2017, Vol 19, Issue 12, p696

1099-4300

Academic Journal

10.3390/e19120696