User:Macumba/Wild Sandbox

The Clopper-Pearson interval is an exact interval since it is based directly on the binomial distribution rather than any approximation to the binomial distribution. This interval, however, can be conservative because of the discrete nature of the binomial distribution. For example, the true coverage rate of a 95% Clopper-Pearson interval may be well above 95%, depending on n and θ. Thus the interval may be wider than it needs to be to achieve 95% confidence. In contrast, it is worth noting that other confidence bounds may be narrower than their nominal confidence with, i.e., the Normal Approximation (or "Standard") Interval, Wilson Interval, Agresti-Coull Interval, etc, with a nominal coverage of 95% may in fact cover less than 95%.