Agresti-Coull Interval
The Agresti-Coull interval is another approximate binomial confidence interval.
Given successes in trials, define
and
Then, a confidence interval for is given by
where is the percentile of a standard normal distribution, as before. For example, for a 95% confidence interval, let, so = 1.96 and = 3.84. If we use 2 instead of 1.96 for, this is the "add 2 successes and 2 failures" interval in
Read more about this topic: Binomial Proportion Confidence Interval
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