Bayes Factor Calculator
Compute the JZS Bayes factor (BF10) for a t-test from a t statistic. Quantify the evidence for the alternative and null hypotheses on the Jeffreys scale.
What Is a Bayes Factor?
A Bayes factor compares two hypotheses by the ratio of how well each predicts the observed data. BF10 > 1 means the data are more likely under the alternative hypothesis than under the null; BF10 < 1 means the reverse. Unlike a p-value, a Bayes factor can actively support the null hypothesis.
This calculator uses the JZS (Jeffreys–Zellner–Siow) prior proposed by Rouder and colleagues (2009), the default analysis in software such as JASP. The effect size is assigned a Cauchy prior with scale r; the medium prior (r = 1/√2) is the common default.
The Jeffreys scale is a rough verbal guide: BF10 of 3–10 is moderate evidence, 10–30 strong, 30–100 very strong and above 100 extreme. Values below 1 support the null, with 1/3–1/10 being moderate and smaller values providing strong-to-extreme evidence for the null.
Key Formula
The JZS Bayes factor integrates the likelihood over the prior on the effect size (g ~ inverse-gamma), which induces a Cauchy prior on the standardized effect:
BF₁₀ = ∫ p(data | δ) p(δ) dδ
δ ~ Cauchy(0, r)
How to Use This Calculator
Follow these steps:
- Run a t-test in your favourite statistics software and note the t statistic, the degrees of freedom and the sample sizes.
- Choose the design that matches your analysis (two groups or one sample / paired) and enter the values.
- Read BF10 (evidence for the alternative) and BF01 (evidence for the null), together with the Jeffreys-scale interpretation.
Worked Example
An independent-groups experiment with n1 = n2 = 30 reports t(58) = 2.50:
Frequently Asked Questions
Have another question? Let us know.
What is the difference between a p-value and a Bayes factor?
A p-value is the probability of data at least as extreme as observed, assuming the null is true. A Bayes factor is the likelihood ratio of the two hypotheses given the data. Crucially, a non-significant p-value cannot distinguish "no effect" from "insufficient data", whereas a Bayes factor quantifies evidence for the null directly.
How should I interpret a Bayes factor below 1?
A BF10 below 1 means the data are more consistent with the null hypothesis. The reciprocal BF01 = 1/BF10 quantifies evidence for the null: BF01 of 3–10 is moderate evidence for the null, and higher values indicate strong-to-extreme evidence for no effect.
What is the JZS prior and does my choice of r matter?
The JZS prior places a Cauchy distribution on the standardized effect size. A smaller r (e.g., 1/√2, medium) assumes smaller effects are more plausible and makes it harder to obtain large Bayes factors; a larger r spreads the prior wider. The medium prior is the recommended default, and results are usually robust to this choice.
When should I report BF10 instead of a p-value?
More and more journals welcome Bayes factors alongside p-values because they can quantify evidence for the null and do not depend on optional stopping in the same way. Report both when possible: the p-value for convention and the Bayes factor for evidence strength.
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