The Agresti-Coull Interval Method calculates confidence intervals for proportions. A proportion (p) , defined as ratios is a type of ratio where the numerator is contained in the denominator. This statistical method . Proportions can be expressed as percentages (per 100), per 1000, or per 100,000, etc. The Agresti-Coull Interval Method was created by two statisticians, Alan Agresti and Brent Coull, who suggested adding 4 observations to the sample, two successes and two failures, and then using the Wald formula to construct a 95% confidence interval (CI).1 In other words, 2 counts are added to the numerator and 4 counts are added to the denominator.
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where X represents the number of observations that belong to a certain category of interest, n represents the denominator (total number of observations), and X/n is the proportion of interest (p).
The Agresti-Coull interval does not show the persistently chaotic coverage probabilities that characterize the standard Wald interval even when the denominator is large and p is not near it’s boundaries (0% or 100%).1,2,3 Other advantages of the Agresti-Coull interval are the following: 1) mean coverage probability is very close to 95%, 2) minimum coverage never dips below 92% for n >10, 3) the expected interval lengths are reasonable, 4) simple, straightforward method, and 5) well-regarded and recommended among statisticians.1,2,3
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