Coverage probability

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

Suppose we are interested in the mean number of months, the common people with a certain type of cancer after successful treatment with chemotherapy remain in remission. The confidence interval is designed according to its construction from it, with a certain probability of containing the unknown median duration of remission. This is the " confidence interval ", which is used as a nominal coverage probability in the construction of the confidence interval and is often selected at 95 percent. The coverage probability is now the actual probability that the resulting time interval ( in this example) contains the true mean duration of remission.

If all are met in the construction of the assumptions used in the confidence interval, the nominal coverage probability will coincide with the ( actual ) coverage probability. This is not, however, where, it may be smaller or larger than the nominal, the actual coverage probability. If the actual coverage probability is greater than the nominal, the interval and the method of its calculation is referred to as "conservative". A discrepancy between the actual and the nominal coverage probability is most common in the approximation of a discrete distribution by a continuous. The construction of binomial confidence intervals is a classic example where the actual and nominal coverage probability rarely coincide.

The concept of probability in the coverage probability refers to a set of hypothetical repetitions of the entire data acquisition and analysis process. These hypothetical repetitions independent records with the same probability distribution as the actual data to be considered, and calculates a confidence interval for each of these data sets.