Confidence Interval For A Proportion

Compute a Wilson score confidence interval for a binary proportion or nonconformance rate.

Concept

Results

Enter the inputs and select Calculate.

Inputs

MethodWilson score interval is the supported method.Confidence level *

Sample size *

Nonconforming count *

Formula & Variables

p̂ + z²2n± z√(p̂(1 - p̂)n+ z²4n²)1 + z²n

p̂: Observed proportion; [1]
n: Sample size; [1]
z: Normal critical value; [1]

Assumptions

Observations are independent Bernoulli trials.
The count represents binary outcomes out of the entered sample size.

⚠ Limitations

Raw data processing, paired intervals, and two-sample intervals require separate methods.
Exact binomial intervals require a separate exact-binomial method and are not included here.