522 – Contributed Poster Presentations: Section on Physical and Engineering Sciences
Finite Population Agresti-Coull Based Binomial Confidence Intervals and Excel VBA Function
William V. Harper
Otterbein University
Agresti-Coull (1998) developed an improvement over the classical central limit theorem based confidence interval for a single binomial proportion; however, it is based on the assumption of an infinite population. The 2nd edition (2013) of API-1163 used in the oil/gas industry to compare in-line inspection tools to excavated corrosion anomalies introduced the Agresti-Coull approach to the pipeline industry. While the exact Clopper-Pearson (1934) binomial confidence interval approach avoids many of the issues of any central limit theorem approximations (including Agresti-Coull) its coverage often exceeds the stated confidence level. For example 95% confidence intervals may average (say) 96% coverage while the Agresti-Coull intervals more closely track to the desired coverage level. In the oil/gas industry small sample sizes are not uncommon and the calling population is often finite. This paper expands the Agresti-Coull method to accommodate finite populations. In addition an Excel VBA function has been developed that creates Agresti-Coull single population binomial confidence intervals as well as expansions beyond the one-tailed upper bound used in API 1163.