Critical review and comparison of continuity correction methods: The normal approximation to the binomial distribution

We provide a comprehensive and critical review of Yates’ continuity correction for the normal approximation to the binomial distribution, in particular emphasizing its poor ability to approximate extreme tail probabilities. As an alternative method, we also review Cressie's finely tuned continuity correction. In addition, we demonstrate how Yates’ continuity correction is used to improve the coverage probability of binomial confidence limits, and propose new confidence limits by applying Cressie's continuity correction. These continuity correction methods are numerically compared and illustrated by data examples arising from industry and medicine.