Bayes factors cannot provide evidence for the null hypothesis

It is becoming increasingly common in the psychology and neuroscience literature to use Bayes factors to provide evidence in favor of the null hypothesis. The most common approach reports a Bayes factor that compares the null hypothesis to a “default” alternative. This approach can show that the data is more likely to have been generated under the null hypothesis than under the specific alternative tested, but it cannot provide evidence for the absence of an effect. In fact, analyses using default alternatives can return evidence in favor of the null hypothesis when the data is consistent with medium to large effects. I show that common interpretations of these Bayes factor analyses are misleading, and I provide examples and simulations that help to understand what a Bayes factor in favor of the null does and does not tell us. I argue that Bayes factors have no special ability to help us understand null effects when compared to frequentist methods such as equivalence testing and confidence intervals.

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Publication Details

Published
2025-09-27
DOI
https://doi.org/10.31234/osf.io/d6u5p_v3
Primary Topic
Meta-analysis and systematic reviews
Type
article
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article

Bayes factors cannot provide evidence for the null hypothesis

Eric C. Fields
Meta-analysis and systematic reviews
article

Bayes factors cannot provide evidence for the null hypothesis

Eric C. Fields
article en

Abstract

It is becoming increasingly common in the psychology and neuroscience literature to use Bayes factors to provide evidence in favor of the null hypothesis. The most common approach reports a Bayes factor that compares the null hypothesis to a “default” alternative. This approach can show that the data is more likely to have been generated under the null hypothesis than under the specific alternative tested, but it cannot provide evidence for the absence of an effect. In fact, analyses using default alternatives can return evidence in favor of the null hypothesis when the data is consistent with medium to large effects. I show that common interpretations of these Bayes factor analyses are misleading, and I provide examples and simulations that help to understand what a Bayes factor in favor of the null does and does not tell us. I argue that Bayes factors have no special ability to help us understand null effects when compared to frequentist methods such as equivalence testing and confidence intervals.

Openalex Percentile: Top 74%
Meta-analysis and systematic reviews
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