Coverage probability: Difference between revisions

A discrepancy between the coverage probability and the nominal coverage probability frequently occurs when approximating a discrete distribution with a continuous one. The construction of [[Binomial proportion confidence intervalbinomial confidence intervals]] is a classic example where coverage probabilities rarely equal nominal levels.<ref>{{cite journal | last = Agresti| first = Alan | coauthors = Coull, Brent | year = 1998 | title = Approximate Is Better than "Exact" for Interval Estimation of Binomial Proportions | journal = The American Statistician | volume = 52 | number = 2 | pages = 119-126 | url=http://www.jstor.org/stable/2685469}}</ref><ref>{{cite journal | last=Brown | first=Lawrence | coauthors=Cai, T. Tony; DasGupta, Anirban | title=Interval Estimation for a binomial proportion | journal=Statistical Science | year=2001 | volume=16 | number=2 | pages=101-117 | url=http://www-stat.jstorwharton.orgupenn.edu/stable~tcai/2676784paper/Binomial-StatSci.pdf}}</ref><ref>{{cite journal | last = Newcombe| first = Robert | year = 1998 | title = Two-sided confidence intervals for the single proportion: Comparison of seven methods. | journal = Statistics in Medicine | volume = 17 | number = 2 | pages = 857-872 | url=http://www3.interscience.wiley.com/journal/3156/abstract | doi = 10.1002/(SICI)1097-0258(19980430)17:8<857::AID-SIM777>3.0.CO;2-E}}</ref> For the binomial case, several techniques for constructing intervals have been created. The Wilson or Score confidence interval is one well known construction based on the normal distribution. Other constructions include the Wald, exact, Agresti-Coull, and likelihood intervals. While the Wilson interval may not be the most conservative estimate, it produces average coverage probabilities that are equal to nominal levels while still producing a comparatively narrow confidence interval.