# Confidence interval for paired binomial proportions

McNemar's test is commonly used to test whether two correlated proportions differ. Unfortunately this test does not tprovide a confidence interval for the difference in proportions.

The classical Wald statistic which is used for constructing confidence intervals for proportions produces too narrow a confidence interval when the difference in proportions is close to zero or one (Newcombe (1998)). Newcombe, instead, suggests using a modification of Wilson's (1927) method based on a single proportion. Agresti & Kin (2005) also find Wilson's method produces good coverage and also suggest an improved confidence interval may be obtained by a simple modification of the Wald statistic. These are all included in this EXCEL spreadsheet.

References

Agresti A and Min Y (2005) Simple improved confidence intervals for comparing matched proportions. *Statistics in Medicine* **24(5)** 729-740.

Newcombe RG (1998) Improved confidence intervals for the difference between binomial proportions based on paired data. *Statistics in Medicine* **17** 2635-2650.

Lee S & Lee S-C (2007) An improved confidence interval for the population proportion in a double sampling scheme subject to false-positive misclassification, *Journal of the Korean Statistical Society* **36** 275–284. (reference for agrestic-oull method used in above spreadsheet).