A Bayesian t test calculator answers a question a p-value cannot: how strongly do the data favor an effect over no effect, or no effect over an effect? Data Lab in AI for Research runs Bayesian t-tests with the JZS Bayes factor for one-sample, paired and two-sample designs, and a Bayesian proportion with a credible interval. The statistics are calculated in your browser, not generated by the AI, and they cost nothing. It is for students meeting Bayesian statistics for the first time, researchers whose result was "not significant" and who want to know whether that means evidence of no effect, and anyone asked by a reviewer for a Bayes factor.
What it does
| Test | Use it for | What you get |
|---|---|---|
| Bayesian one-sample t-test | One group's mean against a fixed value | JZS Bayes factor (BF10 and BF01) |
| Bayesian paired t-test | Before and after, or two matched measurements | JZS Bayes factor (BF10 and BF01) |
| Bayesian two-sample t-test | Two independent groups | JZS Bayes factor (BF10 and BF01) |
| Bayesian proportion (beta-binomial) | A proportion, such as a response rate | The posterior distribution of the proportion and its credible interval |
The t-tests use the Jeffreys-Zellner-Siow (JZS) prior described by Rouder and colleagues (2009), a Cauchy prior on the standardized effect size. The proportion uses a beta prior updated with your successes and failures.
Calculated, not generated
The AI never produces the numbers. Every Bayes factor and interval is computed by code in your browser from your data. The AI is used only if you ask for a written results paragraph, and that paragraph is built from the computed results.
Your file is read in your browser and the tests run there. Download PDF report puts the results, tables and charts in one PDF, free.
How to read a Bayes factor
BF10 is the evidence for the alternative over the null; BF01 is its reciprocal, the evidence for the null. A value of 1 means the data do not favor either. Many researchers describe the size of a Bayes factor with labels like these, adapted from Jeffreys:
| BF10 | BF01 | Common label |
|---|---|---|
| 1 to 3 | 1 to 3 | Anecdotal or weak |
| 3 to 10 | 3 to 10 | Moderate |
| 10 to 30 | 10 to 30 | Strong |
| above 30 | above 30 | Very strong or extreme |
The labels are a convention, not a rule. Report the number itself, and say which prior produced it. A credible interval is read directly: given the prior and the data, there is a 95% probability that the true value lies inside a 95% credible interval. That is the statement many people wrongly make about a confidence interval.
How it works, step by step
- Open Data Lab and load your data: upload a CSV or TSV file, or paste rows copied from a spreadsheet.
- Choose the Bayesian test that fits the design: one-sample, paired, two-sample, or a proportion.
- Pick the columns: the outcome, and the group or the paired measurement. For a one-sample test, enter the comparison value; for a proportion, the column of successes and failures or the counts.
- Read the result: BF10 (evidence for an effect), BF01 (evidence for no effect), and for the proportion the posterior estimate with its credible interval.
- Optionally press for the AI results write-up (2 credits) to get a paragraph you can edit.
- Press Download PDF report to save the tables, charts and write-up as one PDF.
If you are not sure which test you need, start with which statistical test to use.
A worked example
Example (invented for illustration): a psychology master's student tested whether a 10-minute breathing exercise lowers exam anxiety. Two groups of 30 students; the classical t-test gave p = 0.41.
- She loads the CSV into Data Lab and runs the Bayesian two-sample t-test on the anxiety scores by group. Cost: 0 credits.
- The result shows a BF01 of about 3: the data are about three times more likely under no difference than under the alternative, with the default prior. In her discussion she can now say the data give moderate evidence of no effect (a common convention calls 3 to 10 "moderate"), instead of only "not significant". (The numbers here are invented to show how the result reads.)
- She also reports the proportion of students who said they would use the exercise again, 21 of 30, with the Bayesian proportion: a posterior estimate and its credible interval. Cost: 0 credits.
- She asks for the AI results write-up: 2 credits. She edits it, then downloads the PDF report for her supervisor: 0 credits.
Total: 2 credits, inside the Free plan's 45 a month.
What it does not do
- It does not fit full Bayesian models. No Bayesian regression, ANOVA, hierarchical models or MCMC sampling.
- It does not choose a prior for you beyond the default. If your field has an informed prior, note it and run the analysis in a package that accepts it.
- It does not replace a statistician or statistical software. The tests are calculated, not validated or certified for regulatory use.
- It does not tell you what to conclude. A Bayes factor is evidence for one hypothesis relative to another, under the prior you used; report both.
Who uses it
- Master's and PhD students adding a Bayesian analysis to a thesis: see AI for master's students and AI for PhD students.
- Psychology, education and health researchers reporting evidence for the null: see social sciences research and AI for medicine.
- Undergraduates learning Bayesian statistics for beginners alongside a course: see AI for undergraduates.
Data Lab also runs the frequentist tests, charts and sample size calculations; see the Data Lab page. For a quick analysis without an account, try the free data analysis tool.
Learn more
- Bayes factors explained
- The Bayesian t-test, step by step
- Which statistical test to use
- Statistical power and sample size
Last updated 2026-11-13