Bayes Factor Calculator
Turn reported statistics into Bayes factors: a t value and sample sizes (JZS t-test), a correlation and n, or the BIC values of two models. Useful for re-analysing published results.
Updated · By Bibin XavierData 90 × 12
| IDtext · 90 levels | Grouptext · 3 levels | Gendertext · 2 levels | Agenumeric | Hours_Studynumeric | Anxietynumeric | Motivationnumeric | Pre_Scorenumeric | Post_Scorenumeric | Exam_Scorenumeric | Passednumeric · coded | Satisfactionnumeric · coded |
|---|---|---|---|---|---|---|---|---|---|---|---|
| S001 | Control | Male | 23 | 11.2 | 29 | 4.6 | 60 | 62 | 67 | 1 | 2 |
| S002 | Workshop | Female | 23 | 3.9 | 28 | 3.5 | 54 | 70 | 54 | 0 | 2 |
| S003 | Online | Female | 18 | 10.1 | 32 | 4 | 55 | 57 | 66 | 0 | 3 |
| S004 | Control | Male | 26 | 13.6 | 41 | 3.5 | 52 | 55 | 59 | 0 | 3 |
| S005 | Workshop | Female | 22 | 9.7 | 27 | 3.6 | 56 | 63 | 65 | 0 | 4 |
| S006 | Online | Female | 20 | 7.9 | 32 | 3.8 | 65 | 82 | 65 | 0 | 2 |
| S007 | Control | Female | 20 | 6.3 | 28 | 3 | 72 | 83 | 61 | 0 | 3 |
| S008 | Workshop | Male | 22 | 8 | 29 | 3.1 | 64 | 72 | 62 | 1 | 3 |
Variables and options
Results
Calculated in your browserBayes factors
| Hypothesis test | BF10 | BF01 | ln BF10 | Evidence |
|---|---|---|---|---|
| Two-sided H₁: δ ≠ 0 | 3.379 | 0.296 | 1.218 | moderate evidence for H₁ |
| One-sided H₁: δ > 0 | 6.674 | 0.150 | 1.898 | moderate evidence for H₁ |
| One-sided H₁: δ < 0 | 0.084 | 11.930 | -2.479 | strong evidence for H₀ |
Note. JZS Bayes factor (Rouder et al., 2009), Cauchy prior r = 0.707, t(58) = 2.50. Posterior median δ = 0.56, 95% CrI [0.07, 1.08].
Bayes factor robustness check
Interpretation
BF10 = 3.379: the data are 3.38 times more likely under H₁, moderate evidence for H₁ (Lee & Wagenmakers, 2013).
How to cite this tool
Using these results in a thesis, journal article, report or class assignment? Please cite this free tool so others can find it. It keeps the site free.
APA 7
Xavier, B. (2026). Bayes Factor Calculator [Web application]. FreeStatisticalTools.com. https://freestatisticaltools.com/bayes-factor-calculator/
BibTeX
@software{xavier_bayesfactorcalculator_2026,
author = {Xavier, Bibin},
title = {Bayes Factor Calculator},
publisher = {FreeStatisticalTools.com},
year = {2026},
url = {https://freestatisticaltools.com/bayes-factor-calculator/},
note = {Web application}
}Suggested sentence for your methods section: “The analysis was carried out with the free Bayes Factor Calculator tool on FreeStatisticalTools.com (Xavier, 2026).”
What is a Bayes factor?
This calculator turns summary statistics into Bayes factors. From a t value and sample sizes it computes the JZS Bayes factor of Rouder et al. (2009); from a correlation and n, the Bayes factor of Ly et al. (2016); and from the BIC values of two models, the approximation BF₁₀ ≈ exp(ΔBIC / 2).
When to use a Bayes factor
Use it to express published or already-computed results as Bayes factors, for example when reviewing a paper, writing a meta-analysis or checking whether a non-significant result supports the null.
How to set up your data
Summary statistics only: a t value with sample sizes, a correlation with n, or two BIC values.
How to use this calculator
- Enter the values. Fill in start from, design, t value, n (group 1 and or total for one sample / paired).
- Read the results. Results update automatically. Read the plain-English interpretation, then use Copy table to paste APA-style tables into Word and Copy for the results sentence.
How to report a Bayes factor in APA style
“Re-analysing the reported t(58) = 2.50 gave BF₁₀ = 3.0, only moderate evidence for the effect.”
Frequently asked questions
How do I calculate a Bayes factor from a t-test?
Enter t and the sample sizes, choose independent or paired / one-sample design and a prior width. The calculator integrates over the Cauchy prior to give BF₁₀.
How is a Bayes factor computed from BIC?
BF₁₀ ≈ exp((BIC₀ − BIC₁) / 2), where BIC₀ belongs to the null model (Wagenmakers, 2007). It corresponds to a unit-information prior.
What Bayes factor is significant?
There is no fixed cut-off, but BF₁₀ above 3 is commonly called moderate and above 10 strong evidence for H₁; below 1/3 is moderate evidence for H₀.
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