Update an experiment’s binary error rate with a Beta prior and observed failures. This tool shows the posterior expected error rate, a conservative upper credible bound, expected errors per thousand trials, and the amount of evidence in the posterior. It is designed for quality monitoring, model evaluation, and operational experiments where an error is recorded as a yes-or-no event.
Posterior error parameters are α′ = α + errors and β′ = β + trials − errors. Posterior mean = α′/(α′+β′). The upper bound is mean + z times the posterior standard deviation, capped at 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 8 errors in 200 trials and a Beta(1,19) prior, the posterior is Beta(9,211). The posterior mean error rate is 4.09%, or about 40.91 expected errors per 1,000 trials.
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. |