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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 "anticonservative", or "permissive."
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
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.
