Coverage probability: Difference between revisions
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In statistics, the '''coverage probability''' of a [[confidence interval]] is the proportion of the time that the interval contains the true value of interest.<ref>Dodge, Y. (2003) ''The Oxford Dictionary of Statistical Terms'', OUP. ISBN 0199206139</ref> For example, suppose our interest is in the [[expected valuemean]] number of months that people with a particular type of [[cancer]] remain in remission following successful treatment with [[chemotherapy]]. The confidence interval aims to contain the unknown mean remission duration with a given probability. This is the "confidence level" or "confidence coefficient" of the constructed interval which is effectively the "nominal coverage probability" of the procedure for constructing confidence intervals. The "nominal coverage probability" is often set at 0.95. The ''coverage probability'' is the actual probability that the interval contains the true mean remission duration in this example.
If all assumptions used in deriving a confidence interval are met, the nominal coverage probability will equal the coverage probability (termed "true" or "actual" coverage probability for emphasis). If any assumptions are not met, the actual coverage probability could
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  doi = 10.2307/2685469  issue = 2}}</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  issue=2  pages=101–117  url=http://wwwstat.wharton.upenn.edu/~tcai/paper/BinomialStatSci.pdf  doi=10.1214/ss/1009213286}}</ref><ref>{{cite journal  last = Newcombe first = Robert  year = 1998  title = Twosided 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)10970258(19980430)17:8<857::AIDSIM777>3.0.CO;2E  pmid = 9595616  issue = 8}}</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, AgrestiCoull, 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.
