Coverage probability

In statistics, which gives coverage probability of the confidence interval , the probability that the confidence interval contains the true value.

For example, let's say we are interested in the median number of months people with a particular type of cancer remain in remission after successful treatment with chemotherapy . According to its construction, the confidence range aims to contain the unknown mean remission duration with a certain probability. This is the “confidence level” that is used as the nominal coverage probability when constructing the confidence interval and is often chosen at 95 percent. The coverage probability is now the actual probability that the resulting time interval (in this example) contains the true mean remission duration.

If all the assumptions used in the construction of the confidence interval are met, the nominal coverage probability will coincide with the (actual) coverage probability. If, however, this is not the case, the actual coverage probability can be smaller or larger than the nominal. If the actual coverage probability is greater than the nominal, the interval or the method for calculating it is called "conservative". A discrepancy between the actual and the nominal coverage probability often occurs when a discrete distribution is approximated by a continuous one. The construction of binomial confidence intervals is a classic example in which the actual and nominal coverage probabilities rarely match.

The notion of probability in coverage probability refers to a set of hypothetical iterations of the entire data acquisition and analysis process. These hypothetical iterations consider independent data sets with the same probability distribution as the actual data, and calculate a confidence interval for each of these data sets.

See also

• Confidence interval for the probability of success of the binomial distribution

Individual evidence

1. ^ Alan Agresti, Coull, Brent: Approximate Is Better than "Exact" for Interval Estimation of Binomial Proportions . In: The American Statistician . 52, No. 2, 1998, pp. 119-126. JSTOR 2685469 . doi : 10.2307 / 2685469 .
2. ↑ Lawrence Brown, Cai, T. Tony; DasGupta, Anirban: Interval Estimation for a binomial proportion . In: Statistical Science . 16, No. 2, 2001, pp. 101-117. doi : 10.1214 / ss / 1009213286 .
3. ^ Robert Newcombe: Two-sided confidence intervals for the single proportion: Comparison of seven methods. . In: Statistics in Medicine . 17, No. 2, issue 8, 1998, pp. 857-872. doi : 10.1002 / (SICI) 1097-0258 (19980430) 17: 8 <857 :: AID-SIM777> 3.0.CO; 2-E . PMID 9595616 .