Coverage probability: Difference between revisions

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In statistics, the '''coverage probability''' of a technique for calculating 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|0-19-920613-9}}</ref> For example, suppose our interest is in the [[expected value|mean]] 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 either be less than or greater than the nominal coverage probability. When the actual coverage probability is greater than the nominal coverage probability, the interval is termed "conservative", if it is less than the nominal coverage probability, the interval is termed "anti-conservative", or "permissive."