Exact Confidence Range for Binomial Proportion
Calculate conservative Clopper–Pearson interval for success proportion.
Your numbers
Lower end of the range
Use consistent units. Result follow the assumptions wey you enter.
Compare scenarios
You fit keep up to three snapshots for this tab. Loading one go replace the present inputs.
Formula
Use L = B⁻¹(α/2;k,n−k+1) and U = B⁻¹(1−α/2;k+1,n−k). k na successes and n na trials. For confidence-level fraction c, set α = 1−c; B⁻¹ na beta quantile. Handle di boundaries k = 0 → L = 0 and k = n → U = 1.
Calculate conservative Clopper–Pearson interval for success proportion.
Example wey show the calculation
- Number of successes
- 5
- Number of trials
- 10
- Di confidence level (%)
- 95
- Lower end of the range
- 18.7086028447 %
- Upper end of the range
- 81.2913971553 %
- Proportion wey the trials show
- 50 %
Where e fit work and limits
Use consistent units. Result follow the assumptions wey you enter.
We check inputs for missing values and allowed ranges. Result wey pass the finite numeric range no go show. Rounding affect wetin display, while calculation use the model numeric precision.
Check your units and assumptions before you rely on result. Changing label no convert currency or physical unit.
Version of di formula: e318a0d0d050 · Example don get check: