# Proportion Confidence Interval Calculator

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

#### Proportion confidence interval calculator

When using sample data, we know the sample statistic for the proportion, but we do not know the true value of the population's proportion. Instead, we can 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 level of certainty that the true value will fall within the confidence interval. Researchers commonly use a confidence level of 0.95.
The Wilson score interval produces better results than the Clopper–Pearson exact or the normal approximation, especially for small samples and for proportions close to 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 = 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.
##### Results
1. Clopper–Pearson - this is the exact calculation base on the binomial distribution and calculated with the beta distribution. Despite the fact that this method uses the correct distribution. This is not the best method!
2. Normal approximation - this method uses the normal distribution to approximate the binomial distribution. Since it is simple, and relatively good, students usually expected to use the normal approximation. The normal approximation requires a large sample size, as a rule of thumb at least 30. Students usually expected to use the normal approximation method.
3. Wilson score interval - based on the normal approximation, but with modifications.
The Wilson score interval is the best method to estimate the proportion confidence interval.
4. Wilson score interval with continuity correction - similar to the 'Wilson score interval' method, but with a continuity correction to account for the fact that we are using a continuous normal distribution for a discrete binomial distribution.
This supports similar results to the 'Clopper–Pearson' method.