Proportion Confidence Interval Calculator

Proportion confidence interval calculator with calculation steps, using the normal distribution approximation, binomial distribution, and the Wilson score interval.

Proportion confidence interval calculator

When using the sample data, we know the proportion sample statistic but we don't know the true value of the population's proportion. Instead, we may treat the population's measures as random variables and calculate the confidence interval.
First, we need to define the confidence level which is the required certainty level that the true value will be in the confidence interval Researchers commonly use a confidence level of 0.95.
The Wilson score interval supports a better result than the Clopper–Pearson exact, or the normal approximationl, especially for small samples and for edge proportions near 0 or 1.

How to use the proportion confidence interval calculator?
  1. Confidence level - The certainty level that the true value of the estimated parameter will be in the confidence interval, usually 0.95.
  2. Sample size - the number of subjects.
  3. Sample proportion (p̂) or #successes: If the value you entered is between 0 and 1 - the calculator assumed that you enter proportion (proabability).
    When the value is 1, or larger - the calculator assumed that you enter the number of successes.
    For example, when the sample size is 12 if you enter 3 the tool assumes 3 successes, x=3, and will calculate p̂ = 3/12 = 0.25.
    If you enter 0.25, the tool assumes p̂ = 3/12 = 0.25, and the confidence interval will be the same.
  4. Rounding - how to round the results?
    When a resulting value is larger than one, the tool rounds it, but when a resulting value is less than one the tool displays the significant figures.