- Coverage probability
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 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."
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 confidence intervals 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 or Score confidence interval is one well known construction based on the normal distribution. Other constructions include the Wald, exact, Agresti-Coull, 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.
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, 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.
- ^ Dodge, Y. (2003) The Oxford Dictionary of Statistical Terms, OUP. ISBN 0-19-920613-9
- ^ Agresti, Alan; Coull, Brent (1998). "Approximate Is Better than "Exact" for Interval Estimation of Binomial Proportions". The American Statistician 52 (2): 119–126. doi:10.2307/2685469. JSTOR 2685469.
- ^ Brown, Lawrence; Cai, T. Tony; DasGupta, Anirban (2001). "Interval Estimation for a binomial proportion". Statistical Science 16 (2): 101–117. doi:10.1214/ss/1009213286. http://www-stat.wharton.upenn.edu/~tcai/paper/Binomial-StatSci.pdf.
- ^ Newcombe, Robert (1998). "Two-sided confidence intervals for the single proportion: Comparison of seven methods.". Statistics in Medicine 17 (8): 857–872. doi:10.1002/(SICI)1097-0258(19980430)17:8<857::AID-SIM777>3.0.CO;2-E. PMID 9595616. http://www3.interscience.wiley.com/journal/3156/abstract.
Wikimedia Foundation. 2010.
Look at other dictionaries:
Coverage — may refer to: Contents 1 Filmmaking 2 Media and journalism 3 Music … Wikipedia
Imprecise probability — The notion of Imprecise probability is used as a generic term to cover all mathematical models which measure chance or uncertainty without sharp numerical probabilities. It includes both qualitative (comparative probability, partial preference… … Wikipedia
Media coverage of the Iraq War — Journalist Geraldo Rivera who while with the 101st Airborne Division during war with Iraq in 2003 began to disclose an upcoming operation drawing a map in the sand for his audience. The 2003 invasion of Iraq involved unprecedented media… … Wikipedia
Sticking probability — The sticking probability is the probability that molecules are trapped on surfaces and adsorb chemically. From Langmuir s adsorption isotherm, molecules cannot adsorb on surfaces when the adsorption sites are already occupied by other molecules,… … Wikipedia
Measurement uncertainty — In metrology, measurement uncertainty is a non negative parameter characterizing the dispersion of the values attributed to a measured quantity. The uncertainty has a probabilistic basis and reflects incomplete knowledge of the quantity. All… … Wikipedia
Confidence band — A confidence band is used in statistical analysis to represent the uncertainty in an estimate of a curve or function based on limited or noisy data. Confidence bands are often used as part of the graphical presentation of results in a statistical … Wikipedia
Likelihood function — In statistics, a likelihood function (often simply the likelihood) is a function of the parameters of a statistical model, defined as follows: the likelihood of a set of parameter values given some observed outcomes is equal to the probability of … Wikipedia
Confidence interval — This article is about the confidence interval. For Confidence distribution, see Confidence Distribution. In statistics, a confidence interval (CI) is a particular kind of interval estimate of a population parameter and is used to indicate the… … Wikipedia
Multiple comparisons — In statistics, the multiple comparisons or multiple testing problem occurs when one considers a set of statistical inferences simultaneously. Errors in inference, including confidence intervals that fail to include their corresponding… … Wikipedia
Binomial proportion confidence interval — In statistics, a binomial proportion confidence interval is a confidence interval for a proportion in a statistical population. It uses the proportion estimated in a statistical sample and allows for sampling error. There are several formulas for … Wikipedia