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

ABSTRACT

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.

KEYWORDS:

• Central limit theorem
• Confidence limit
• Control chart
• Statistical process control
• Yates’ correction

Acknowledgments

We thank the reviewer for his/her constructive suggestions about confidence intervals for binomial proportion. We also thank my three colleagues (Professors Cheng-Der Fuh, Huei-Wen Teng, and Li-Hsien Sun) for their comments on the earlier version of our manuscript and for Professor Nan-Cheng Su for his comments when our paper was presented at the 25th South Taiwan Statistics Conference. Our work is supported by the Taiwan government (MOST 103-2118-M-008-MY2; MOST 105-2118-M-008-003-MY2).

Author contribution

• Emura T: Designed and supervised the study. Wrote and revised the manuscript (all sections). Conducted numerical analyses (Section 4).

• Liao YT: Wrote and revised the manuscript (all sections). Conducted numerical analyses (Sections 2 and 3).