The Confidence Interval of a Proportion
This unit will calculate the lower and upper limits of the 95% confidence interval for a proportion, according to two methods described by Robert Newcombe, both derived from a procedure outlined by E. B. Wilson in 1927 (references below). The first method uses the Wilson procedure without a correction for continuity; the second uses the Wilson procedure with a correction for continuity.

For the notation used here, n = the total number of observations and k = the number of those n observations that are of particular interest. Thus, if one observes 23 recoveries among 60 patients, n = 60, k = 23, and the proportion is 23/60 = 0.3833.

To calculate the lower and upper limits of the confidence interval for a proportion of this sort, enter the values of k and n in the designated places, then click the «Calculate» button.
k =
  Proportion =
n =

95% confidence interval: no continuity correction
Lower limit =
Upper limit =
95% confidence interval: including continuity correction
Lower limit =
Upper limit =

Newcombe, Robert G. "Two-Sided Confidence Intervals for the Single Proportion: Comparison of Seven Methods," Statistics in Medicine, 17, 857-872 (1998).

Wilson, E. B. "Probable Inference, the Law of Succession, and Statistical Inference," Journal of the American Statistical Association, 22, 209-212 (1927).

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