BAYES FACTOR VS. P-VALUE: EVALUATION OF STATISTICAL HYPOTHESES LIKELIHOOD IN PSYCHOLOGY

Abstract

The disadvantages of p-value as a statistical tool are considered, they are: relation with hypothetical data and researcher’s intentions, dependence on the sample size, the lack of statistical evidence. Interpretive definitions of p-value are opposed a rigorous mathematical definition: p-value as the probability of the data obtained in the study under the condition of the null hypothesis truth. Alternative measure to evaluate the statistical hypotheses likelihood – Bayes factor or likelihood ratio – is presented. Its mathematical and descriptive understanding is outlined. Bayes factor is the ratio of the probability of the data under the condition of the truth of one hypothesis to the probability of the data under the condition of the truth of other. The methods of its interpretation are provided: simple mathematical and based on the evidence conception. The formula of transition from Bayes factor to the assessment of the hypothesis probability under the condition of the data obtained in the study is also considered. The advantages of this factor are shown in the example of research practice in which the use of classical frequentist approach leads to wrong interpretations (absence, presence of differences), although the use of Bayes factor shows insufficient evidence for both the null hypothesis and the alternative hypothesis.

Keywords: Bayes factor, p-value, statistics, hypotheses likelihood, frequentist approach, Bayesian approach, methodological pluralism

Accepted: 15.08.2016

Reviewed: 28.08.2016

Published: 06.10.2016