Adaptive Significance Levels in Tests for Linear Regression Models: The e-Value and P-Value Cases.

The full Bayesian significance test (FBST) for precise hypotheses is a Bayesian alternative to the traditional significance tests based on p-values. The FBST is characterized by the e-value as an evidence index in favor of the null hypothesis (H). An important practical issue for the implementation of the FBST is to establish how small the evidence against H must be in order to decide for its rejection. In this work, we present a method to find a cutoff value for the e-value in the FBST by minimizing the linear combination of the averaged type-I and type-II error probabilities for a given sample size and also for a given dimensionality of the parameter space. Furthermore, we compare our methodology with the results obtained from the test with adaptive significance level, which presents the capital-P P-value as a decision-making evidence measure. For this purpose, the scenario of linear regression models with unknown variance under the Bayesian approach is considered.

Uso de pruebas estadísticas inferenciales en la Revista Cubana de Medicina Militar / Use of Inferential Statistical Tests in the Cuban Journal of Military Medicine

Introducción: desde hace años, existe un debate sobre el uso de las pruebas estadísticas inferenciales en los reportes de resultados de investigación, se destaca la crítica al empleo de las pruebas de significación estadística y sus limitaciones. Objetivos: determinar la frecuencia de empleo de las pruebas de significación estadística (PSE) e intervalos de confianza (IC) por tipos de estudio publicado, cómo se reflejan los resultados de estas, la influencia del tamaño de la muestra, así comosu vinculación con las conclusiones. Resultados: en el periodo 2010 - 2015 de 150 artículos originales, 98 por ciento fueron descriptivos o explicativos y de ellos, el 95 por ciento emplea las PSE, solas o con IC. Predomina el uso de las PSE solas (69 por ciento de los trabajos). En el 25 por ciento se explica la selección del nivel de significación utilizado y el 53 por ciento de los estudios reflejan las cifras exactas de las pruebas realizadas. Solo el 15 por ciento menciona la influencia del tamaño de la muestra en relación con los resultados de las pruebas estadísticas. En las conclusiones, el 86 por ciento de los artículos se refieren adecuadamente a los objetivos del estudio. Conclusiones: predomina el uso de las PSE e IC, fundamentalmente de las PSE, más de la mitad de los trabajos mencionan los resultados precisos de las pruebas, la mayoría no argumenta la relación de estos resultados con el tamaño de la muestra y los autores elaboran las conclusiones de acuerdo con los objetivos planteados en el estudio(AU)

Introduction: For years there has been a debate about the use of inferential statistical tests in the reports of research results, highlighting the criticism to the use of tests of statistical significance and its limitations. Objectives: To determine the frequency of use of statistical significance tests (SST) and confidence intervals (CI) by published study types, how the results are reported, and the influence of sample size, as well as their relationship with the conclusions. Results: In the period 2010-2015 of 150 original articles, 98 percent were descriptive or explanatory and of them, 95 percent used SST alone or with CI. The use of SST alone (69 percent of the articles) predominates. In 25 percent the significance level selection is explained and 53 percent of the studies reflect the exact figures of the tests performed. Only 15 percent mentions the influence of sample size on the results of statistical tests. In the conclusions, 86 percent of the articles refer adequately to the objectives of the study. Conclusions: SST and CI use predominate, mainly SST, more than half of the studies mention the precise results of the tests, most do not argue the relation of these results to the sample size and the authors elaborate the conclusions in accordance with the objectives set out in the study(AU)

Genuine Bayesian multiallelic significance test for the Hardy-Weinberg equilibrium law

Statistical tests that detect and measure deviation from the Hardy-Weinberg equilibrium (HWE) have been devised but are limited when testing for deviation at multiallelic DNA loci is attempted. Here we present the full Bayesian significance test (FBST) for the HWE. This test depends neither on asymptotic results nor on the number of possible alleles for the particular locus being evaluated. The FBST is based on the computation of an evidence index in favor of the HWE hypothesis. A great deal of forensic inference based on DNA evidence assumes that the HWE is valid for the genetic loci being used. We applied the FBST to genotypes obtained at several multiallelic short tandem repeat loci during routine parentage testing; the locus Penta E exemplifies those clearly in HWE while others such as D10S1214 and D19S253 do not appear to show this.