# A tutorial on testing hypotheses using the Bayes factor.

@article{Hoijtink2019ATO, title={A tutorial on testing hypotheses using the Bayes factor.}, author={Herbert Hoijtink and Joris Mulder and Caspar J. van Lissa and Xin Gu}, journal={Psychological methods}, year={2019} }

Learning about hypothesis evaluation using the Bayes factor could enhance psychological research. In contrast to null-hypothesis significance testing it renders the evidence in favor of each of the hypotheses under consideration (it can be used to quantify support for the null-hypothesis) instead of a dichotomous reject/do-not-reject decision; it can straightforwardly be used for the evaluation of multiple hypotheses without having to bother about the proper manner to account for multiple…

## Figures from this paper

## 60 Citations

How to Choose between Different Bayesian Posterior Indices for Hypothesis Testing in Practice.

- PsychologyMultivariate behavioral research
- 2021

This comparison shows that conceptually not all proposed Bayesian alternatives to NHST and $p$-values are beneficial, and the usefulness of some indices strongly depends on the study design and research goal, but reveals that there exist at least two candidates among the available Bayesian posterior indices which have appealing theoretical properties and are, to the best knowledge, widely underused among psychologists.

BFpack: Flexible Bayes Factor Testing of Scientific Theories in R

- Computer ScienceJ. Stat. Softw.
- 2021

A new R-package called BFpack is presented that contains functions for Bayes factor hypothesis testing for the many common testing problems and includes novel tools for Bayesian confirmatory testing.

The Full Bayesian Significance Test and the e-value -- Foundations, theory and application in the cognitive sciences

- Psychology
- 2020

Hypothesis testing is a central statistical method in psychological research and the cognitive sciences. While the problems of null hypothesis significance testing (NHST) have been debated widely,…

Improving statistical practice in psychological research: Sequential tests of composite hypotheses

- Psychology
- 2020

Statistical hypothesis testing is an integral part of the scientific process. When employed to make decisions about hypotheses, it is important that statistical tests control the probabilities of…

Bayesian hypothesis testing of mediation: Methods and the impact of prior odds specifications.

- BusinessBehavior research methods
- 2022

Mediation analysis is widely used to study whether the effect of an independent variable on an outcome is transmitted through a mediator. Bayesian methods have become increasingly popular for…

Bayes Factors can only Quantify Evidence w.r.t. Sets of Parameters, not w.r.t. (Prior) Distributions on the Parameter

- Mathematics
- 2021

Bayes factors are characterized by both the powerful mathematical framework of Bayesian statistics and the useful interpretation as evidence quantification. Former requires a parameter distribution…

“Repeated sampling from the same population?” A critique of Neyman and Pearson’s responses to Fisher

- PsychologyEuropean Journal for Philosophy of Science
- 2020

Fisher ( 1945a , 1945b , 1955 , 1956 , 1960 ) criticised the Neyman-Pearson approach to hypothesis testing by arguing that it relies on the assumption of “repeated sampling from the same population.”…

Bayes factor testing of equality and order constraints on measures of association in social research

- SociologyJournal of Applied Statistics
- 2021

Measures of association play a central role in the social sciences to quantify the strength of a linear relationship between the variables of interest. In many applications researchers can translate…

Teacher’s Corner: Evaluating Informative Hypotheses Using the Bayes Factor in Structural Equation Models

- Computer ScienceStructural Equation Modeling: A Multidisciplinary Journal
- 2020

ABSTRACT This Teacher’s Corner paper introduces Bayesian evaluation of informative hypotheses for structural equation models, using the free open-source R packages bain, for Bayesian informative…

Bayesian updating: increasing sample size during the course of a study

- MedicineBMC Medical Research Methodology
- 2021

A simulation study is conducted to study what sample size may be expected and how large the error rate is, that is, how often the Bayes factor shows most support for the hypothesis that was not used to generate the data.

## References

SHOWING 1-10 OF 97 REFERENCES

A tutorial on a practical Bayesian alternative to null-hypothesis significance testing

- PsychologyBehavior research methods
- 2011

A tutorial on a Bayesian model selection approach that requires only a simple transformation of sum-of-squares values generated by the standard analysis of variance and obviates admonitions never to speak of accepting the null hypothesis.

Bayesian t tests for accepting and rejecting the null hypothesis

- BiologyPsychonomic bulletin & review
- 2009

To facilitate use of the Bayes factor, an easy-to-use, Web-based program is provided that performs the necessary calculations and has better properties than other methods of inference that have been advocated in the psychological literature.

Bayesian hypothesis testing for psychologists: A tutorial on the Savage–Dickey method

- PsychologyCognitive Psychology
- 2010

`Is the Hypothesis Correct’ or `Is it not’? Bayesian Evaluation of One Informative Hypthesis in ANOVA.

- Mathematics
- 2013

Researchers in the behavioral and social sciences often have one informative hypothesis with respect to the state of affairs in the population from which they sampled their data. The question they…

Sequential Hypothesis Testing With Bayes Factors: Efficiently Testing Mean Differences

- MathematicsPsychological methods
- 2017

This contribution investigates the properties of a procedure for Bayesian hypothesis testing that allows optional stopping with unlimited multiple testing, even after each participant, and investigates the long-term rate of misleading evidence, the average expected sample sizes, and the biasedness of effect size estimates when an SBF design is applied to a test of mean differences between 2 groups.

Optional stopping: No problem for Bayesians

- BusinessPsychonomic bulletin & review
- 2014

In this article, it is shown through simulation that the interpretation of Bayesian quantities does not depend on the stopping rule, and the proper interpretation ofBayesian quantities as measures of subjective belief on theoretical positions is emphasized.

Bayesian Model Selection in Social Research

- Economics
- 1995

It is argued that P-values and the tests based upon them give unsatisfactory results, especially in large samples. It is shown that, in regression, when there are many candidate independent…

Bayesian evaluation of inequality constrained hypotheses.

- BusinessPsychological methods
- 2014

An approximate Bayes procedure can be used for the selection of the best of a set of inequality constrained hypotheses based on the Bayes factor in a very general class of statistical models and the software package BIG is provided such that psychologists can use the approach for the analysis of their own data.

Bayesian Evaluation of Constrained Hypotheses on Variances of Multiple Independent Groups

- MathematicsPsychological methods
- 2017

This article proposes a novel Bayesian approach to this challenging testing problem that can be used to simultaneously test multiple (non)nested hypotheses with equality as well as inequality constraints on the variances.