Binomial Proportion Confidence Interval - Agresti-Coull Interval

Agresti-Coull Interval

The Agresti-Coull interval is another approximate binomial confidence interval.

Given successes in trials, define

\tilde{n} = n + z_{1- \alpha /2}^2

and

\tilde{p} = \frac{X + z_{1- \alpha /2}^2/2}{\tilde{n}}

Then, a confidence interval for is given by

\tilde{p} \pm z_{1- \alpha /2} \sqrt{\frac{\tilde{p}\left(1 - \tilde{p} \right)}{\tilde{n}}}

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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