Estimate an approximate Bayesian credible interval for a binary experiment after combining observed successes with a Beta prior. The calculator reports the posterior mean, lower and upper bounds, and effective posterior sample size so you can see how strongly the data update your starting belief. It is useful for conversion tests, reliability checks, and other yes-or-no outcomes when a transparent conjugate model is appropriate.
Posterior Beta parameters are α′ = α + successes and β′ = β + trials − successes. Mean = α′/(α′+β′). The displayed bounds use mean ± z√[α′β′/((α′+β′)²(α′+β′+1))], clipped to 0–100%.
The primary result is conditional on the values and statistical assumptions entered. Read the secondary results to understand uncertainty, workload, or design sensitivity before making a decision.
This planning estimate is not a substitute for a study protocol, domain review, or a method chosen for the final data distribution.
With 60 successes in 100 trials and a Beta(1,1) prior, the posterior is Beta(61,41). Its mean is 59.80%, and the approximate 95% interval is about 50.29% to 69.32%.
The calculator uses a standard statistical approximation. Small samples, highly skewed outcomes, or model misspecification can make the estimate less accurate.
Yes. A 90% setting gives a narrower interval or lower sample requirement, while a 95% setting provides more conservative coverage.
Use zero only where the input allows it. A rate calculation still needs a positive total or a defined prior so that division by zero is avoided.
No. It summarizes uncertainty or planning assumptions; study design, randomization, measurement quality, and confounding still matter.
Keep rates and intervals at the shown precision, but round required counts upward because a fraction of a sample or processing unit is not usable.
| Item | How it is used |
|---|---|
| Observed or planned sample | Sets the available evidence or workload. |
| Uncertainty setting | Controls interval width or rejection threshold. |
| Variability or rate | Translates the sample into uncertainty, power, or capacity. |