Bayesian A B Comparison Calculator
Compare two binomial conversion rates using independent beta posteriors and an exact finite-sum superiority probability.
YOUR CALCULATION
Result
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Calculation steps
Work through one step at a time or reveal the complete calculation. The steps use your current inputs.
How to calculate
Update the two independent beta distributions and keep posterior probability distinct from a frequentist p-value.
Posterior A=Beta(α+sA,β+nA−sA), similarly B; evaluate P(pA>pB) with the integer-alpha beta-function sum
Worked example
Equal trial/conversion counts and equal priors give P(pA>pB)=0.5 by symmetry, including zero observed conversions.
Assumptions and input details
Conversions cannot exceed trials. Shared integer beta priors, independent Bernoulli observations and no optional stopping/control for repeated metrics. Credible intervals are marginal 95% equal-tail intervals; no causal lift, decision threshold or future conversion guarantee.
References: Evan Miller: exact beta superiority formulas
Using this calculator
Can I enter my own problem?
Yes. Replace the example values with your own inputs. The result, calculation steps, tables and applicable diagrams update from those inputs. Blank or invalid values clear the result; example values are never silently substituted for missing inputs.
Are the results exact?
Results use floating-point arithmetic and displayed rounding. Read the formula, assumptions and any stated data precision before interpreting the result.
Is my input uploaded?
The calculation runs in your browser. No account, file upload or external AI service is required. Inputs are not saved between page reloads.
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