= 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 [[attachment:paired_pci.xls|spreadsheet.]] 

 * [[FAQ/BinomialCofidence/2gpp/Rcode| Some R code for the Agresti-Min approach above is also available]]

__References__

[[attachment:agresti.pdf|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).