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. For example, suppose our interest is in the [[expected value|mean]] number of months that people with a particular type of [[cancer]] whoremain arein successfullyremission treatedfollowing successful treatment with a particular [[chemotherapy]] remain in remission. The confidence interval aims to contain the unknown mean remission duration with a given probability (the "nominal coverage probability"). The ''coverage probability'' is the actual probability that the interval contains the true mean remission duration. 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 be either be below or above 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."
The "probability" in ''coverage probability'' is interpreted with respect to a set of hypothetical repetitions of the entire data collection and analysis procedure. In these hypothetical repetitions, [[independence (probability theory)|independent]] data sets following the same [[probability distribution]] as the actual data are considered, and a confidence interval is computed from each of these data sets.