ggstatsplot reports Bayes Factors as
:
in the caption for parametric tests (controlled by
bf.message), in the subtitle for
type = "bayes", and on the brackets for Bayesian pairwise
comparisons. This article explains how to read these values.
Bayes Factors (BFs) are a fundamental tool in Bayesian analysis for comparing two hypotheses: typically the null hypothesis (H₀) and the alternative hypothesis (H₁). The Bayes Factor in favor of the null over the alternative is written as BF₀₁, which tells you how many times more likely the observed data are under H₀ than under H₁. For example, a BF₀₁ of 5 means the data are 5 times more likely under the null hypothesis. A BF₀₁ of 0.2 (i.e., 1/5) means the data are 5 times more likely under the alternative hypothesis.
Importantly, Bayes Factors can support either hypothesis:
- BF₀₁ > 1 → evidence favors H₀ (null hypothesis)
- BF₀₁ < 1 → evidence favors H₁ (alternative hypothesis)
- BF₀₁ = 1 → evidence is balanced; neither hypothesis is preferred
This symmetry makes Bayes Factors more flexible than traditional p-values, which can only reject or fail to reject H₀.
Why Use the Natural Log of Bayes Factors?
Instead of reporting the raw BF₀₁ values, it is often better to report their natural logarithm, written as ln(BF₀₁) or log(BF₀₁) with base e. Here’s why:
Compresses Wide Ranges for Simpler Interpretation
Bayes Factors can range from extremely small values (e.g. 0.001) to very large ones (e.g. 1000), which makes them hard to compare directly. Taking the natural log compresses this wide range:
- BF₀₁ = 100 → ln(BF₀₁) ≈ 4.6
- BF₀₁ = 1 → ln(BF₀₁) = 0
- BF₀₁ = 0.01 → ln(BF₀₁) ≈ –4.6
This compression makes values easier to report and visualize, especially when plotting results or summarizing across multiple studies (e.g., meta-analysis).
Symmetrical Evidence Scale
Using the natural log also gives a symmetric scale centered around 0:
- ln(BF₀₁) > 0 → evidence favors H₀
- ln(BF₀₁) < 0 → evidence favors H₁
- ln(BF₀₁) = 0 → evidence is neutral
So, a log BF₀₁ of +2 means data support H₀ about as strongly as –2 would support H₁. This makes interpretation intuitive: zero means balanced evidence, and distance from zero indicates strength regardless of direction.
Interpreting Log Bayes Factors
A commonly used classification scheme (Lee & Wagenmakers, 2014, adapted from Jeffreys, 1961) labels the strength of evidence as follows:
| BF₀₁ | ln(BF₀₁) | Evidence for H₀ |
|---|---|---|
| > 100 | > 4.61 | Extreme |
| 30 – 100 | 3.40 – 4.61 | Very strong |
| 10 – 30 | 2.30 – 3.40 | Strong |
| 3 – 10 | 1.10 – 2.30 | Moderate |
| 1 – 3 | 0 – 1.10 | Anecdotal |
| 1 | 0 | Balanced evidence |
The same labels apply to evidence for H₁ when ln(BF₀₁) is negative (e.g., ln(BF₀₁) between –3.40 and –2.30 is strong evidence for H₁). These labels are only rough guides; the further the value is from 0, the stronger the evidence—positive values favor the null, negative values favor the alternative.
References
- Jeffreys, H. (1961). Theory of Probability (3rd ed.). Oxford University Press.
- Kass, R. E., & Raftery, A. E. (1995). Bayes Factors. Journal of the American Statistical Association, 90(430), 773–795. https://doi.org/10.2307/2291091
- Lee, M. D., & Wagenmakers, E.-J. (2014). Bayesian Cognitive Modeling: A Practical Course. Cambridge University Press.
- Morey, R. D., & Wagenmakers, E.-J. (2014). Simple Relation Between Bayesian Order-Restricted and Point-Null Hypothesis Tests. Statistics & Probability Letters, 92, 121–124. https://doi.org/10.1016/j.spl.2014.05.010
- van Doorn, J., van den Bergh, D., Bohm, U., et al. (2021). The JASP Guidelines for Conducting and Reporting a Bayesian Analysis. Psychonomic Bulletin & Review, 28(3), 813–826. https://doi.org/10.3758/s13423-020-01798-5