Overview
A common problem in basic statistics is the estimation of the proportion of individuals with a certain characteristic of interest in a population. For example, a quality engineer may want to estimate the proportion of defects in a large batch of mass-produced units on a given day; a medical scientist may want to investigate the proportion of individuals in some community who were vaccinated against a specific pathogen but experienced the related disease nonetheless; a campaign manager may be interested in the proportion of registered voters who intend to vote for their candidate.
The best-known interval estimation methods for this problem are the textbook normal approximation method referred to as the Wald confidence interval (CI) and the Clopper-Pearson exact (1934) CI. On one hand, the Wald CI is extremely liberal in that the actual confidence level (or coverage probability) of the CI is well below the targeted nominal level, particularly when the true proportion is close to 0 or 1 (see Figure 1). On the other hand, the exact Clopper-Pearson CI is excessively conservative in that the actual confidence level (or coverage probability) of the CI is well above the targeted nominal level. Both of these methods should no longer be used for any practical applications (see Agresti-Coull, 1998; Brown et al., 2001).
In recent years, however, they have played a major role in the development of better CI methods with better intermediate coverage probabilities. For example, Agresti-Coull approximate CI is an adjustment on the Wald CI; the Blaker (2000, 2001) exact CI uses Clopper-Pearson confidence bounds as starting estimates in an iterative numerical algorithm. Mindful of these newly improved methods, Minitab has updated the statistical tool for estimating a single population proportion to include the following 4 methods: the adjusted Blaker CI and test methods, the Wilson/score CI and test methods (with and without a continuity correction), and the Agresti-Coull CI and test methods. In addition, for each of these methods, Minitab ensures that the CI and test yield consistent results.
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