# Coverage Probability Coverage probability is a way to assess confidence intervals.Coverage probability is the probability a procedure for the construction of a region will give an interval that covers (contains) the true population parameter. In other words, it is the chance a constructed interval contains the parameter you’re interested in .

## The Ideal Coverage Probability

Coverage probability is a way to evaluate the performance of a confidence interval estimator; ideally, your CI should have the highest possible coverage probability . The usual way to choose a coverage probability is by convention or your best judgment, with 90%, 95%, and 99% being typical choices . However, this isn’t easy: larger prediction intervals (e.g., 95%) might contain all of your values, but these tend to be very wide prediction intervals with little practical value. Setting a too-narrow interval may result in all of your values falling outside the interval, which again is not practical. The goal then, is to find the middle ground.

## Coverage Probability vs. Confidence Level

At first glance, coverage probability looks exactly the same as confidence level. However, there are several differences :

• Coverage probability is the probability an interval surrounding the unknown parameter depends on the unknown parameter value; Confidence is the infimum of all coverage probabilities.
• While confidence levels can be calculated by hand, coverage probability is best calculated by computer, as this involves finding the sum of infinite calculations.
• Coverage probabilities tend to be higher than confidence levels if approximations are used to create confidence intervals; Coverage and confidence can be equal when working with continuous distributions (for example, if you’re constructing an interval for the mean of a normally distributed population with a t-distribution ); they are never equal when dealing with discrete distributions (for example, when constructing binomial confidence intervals).