179:. Other constructions include the Wald, exact, Agresti-Coull, and likelihood intervals. While the Wilson score 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.
130:
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
388:
159:. The confidence interval aims to contain the unknown mean remission duration with a given probability. In this example, the coverage probability would be the real probability that the interval actually contains the true mean remission duration.
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is a classic example where coverage probabilities rarely equal nominal levels. For the binomial case, several techniques for constructing intervals have been created. The Wilson score interval is one well-known construction based on the
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of the procedure for constructing confidence intervals. Hence, referring to a "nominal confidence level" or "nominal confidence coefficient" (e.g., as a synonym for
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is interpreted with respect to a set of hypothetical repetitions of the entire data collection and analysis procedure. In these hypothetical repetitions,
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than the nominal coverage probability. When the actual coverage probability is greater than the nominal coverage probability, the interval is termed a
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In prediction, when the coverage probability is equal to the nominal coverage probability, that is known as predictive probability matching.
198:. The coverage probability is the fraction of these computed confidence intervals that include the desired but unobservable parameter value.
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In estimation, when the coverage probability is equal to the nominal coverage probability, that is known as probability matching.
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383:{\displaystyle P\left(T_{u}\leq \vartheta \leq T_{v}\right)\geq \gamma \quad ({\text{for any allowed parameter }}\vartheta )}
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A discrepancy between the coverage probability and the nominal coverage probability frequently occurs when approximating a
540:
Agresti, Alan; Coull, Brent (1998). "Approximate Is Better than "Exact" for
Interval Estimation of Binomial Proportions".
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already. The nominal coverage probability is often set at 0.95. By contrast, the (true) coverage probability is the
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513:
Severini, T; Mukerjee, R; Ghosh, M (2002). "On an exact probability matching property of right-invariant priors".
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as the actual data are considered, and a confidence interval is computed from each of these data sets; see
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The construction of the confidence interval ensures that the probability of finding the true parameter
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628:"Two-sided confidence intervals for the single proportion: Comparison of seven methods"
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in the sense of "nominal" and "actual coverage probability"; cf., for instance,
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135:; if it is less than the nominal coverage probability, the interval is termed
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10.1002/(SICI)1097-0258(19980430)17:8<857::AID-SIM777>3.0.CO;2-E
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Wackerly, Dennis; Mendenhall, William; Schaeffer, Richard L. (2008),
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where the interval surrounds an out-of-sample value as assessed by
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where the interval surrounds the true value as assessed by
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Brown, Lawrence; Cai, T. Tony; DasGupta, Anirban (2001).
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number of months that people with a particular type of
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probability that the interval contains the parameter.
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44:(parameter) of interest. It can be defined as the
671:Recent developments on probability matching priors
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95:pre-specified by the analyst, referred to as the
673:. New York Science Publishers. pp. 227–252.
103:of the constructed interval, is effectively the
577:"Interval Estimation for a binomial proportion"
457:(7th ed.), Cengage Learning, p. 437,
143:. For example, suppose the interest is in the
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490:The Oxford Dictionary of Statistical Terms.
67:will include an out-of-sample value of the
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433:However, some textbooks use the terms
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155:following successful treatment with
133:conservative (confidence) interval
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607:from the original on 23 June 2010
115:and misleading, as the notion of
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371:for any allowed parameter
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55:In statistical prediction, the
669:Ghosh, M; Mukerjee, R (1998).
439:nominal confidence coefficient
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447:actual confidence coefficient
280:{\displaystyle (T_{u},T_{v})}
190:data sets following the same
172:binomial confidence intervals
109:nominal coverage probability
105:nominal coverage probability
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230:{\displaystyle \vartheta }
119:itself inherently implies
626:Newcombe, Robert (1998).
542:The American Statistician
435:nominal confidence level
192:probability distribution
638:(2, issue 8): 857–872.
443:actual confidence level
405:Confidence distribution
300:{\displaystyle \gamma }
77:proportion of instances
46:proportion of instances
632:Statistics in Medicine
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170:. The construction of
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182:The "probability" in
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241:-dependent interval
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202:Probability Matching
184:coverage probability
73:coverage probability
57:coverage probability
22:coverage probability
584:Statistical Science
415:Interval estimation
410:False coverage rate
196:Neyman construction
177:normal distribution
93:degree of certainty
65:prediction interval
34:confidence interval
658:on 5 January 2013.
488:Dodge, Y. (2003).
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81:long-run frequency
50:long-run frequency
28:for short, is the
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476:References
151:remain in
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121:nominality
91:The fixed
42:true value
375:ϑ
363:γ
360:≥
342:≤
339:ϑ
336:≤
295:γ
225:ϑ
153:remission
685:Category
602:Archived
500:, p. 93.
394:See also
26:coverage
652:9595616
611:17 July
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237:in the
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87:Concept
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239:sample
149:cancer
125:actual
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605:(PDF)
580:(PDF)
558:JSTOR
523:JSTOR
492:OUP,
421:Notes
139:, or
24:, or
648:PMID
613:2009
494:ISBN
459:ISBN
145:mean
640:doi
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550:doi
445:or
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