Coverage Probability
Definition
The true long-run proportion of intervals, from repeated sampling, that contain the parameter. If a procedure has 95% nominal coverage and its assumptions are met, coverage probability equals 0.95.
- Field
- Statistics, confidence intervals
- Definition type
- Long-run frequency property, not a single-interval probability
- At correct assumptions
- Matches the nominal confidence level, e.g. 0.95 for a 95% interval
Common questions
Why can't coverage probability be applied to say a specific interval has a 95% chance of containing the true value?+
Coverage probability describes the long-run behaviour of the procedure across many repeated samples, not the probability attached to any single, already-computed interval. Once an interval is calculated, the true parameter either lies inside it or it does not, so the 95% figure describes the method's reliability, not a probability statement about that one result.
What causes actual coverage to fall short of the nominal level in forensic statistical work?+
Coverage probability only equals the nominal level when the assumptions behind the method hold, such as correct distributional assumptions or independence of observations. Violations, for example correlated measurements or a small or non-representative sample, can make the true coverage lower than the stated confidence level implies.
Related terms
- Bayesian Credible Interval
- An interval computed from the posterior distribution of a parameter, given a prior and the observed data. Unlike a confidence interval, a...
- Confidence Interval (CI)
- A range computed from sample data using a procedure that, over many repetitions, would contain the true population parameter a stated percentage...
- Critical Value
- The value from a reference distribution (z or t) that cuts off the desired tail probability. For a 95% two-sided interval using...
- Margin of Error
- Half the width of a symmetric confidence interval, equal to the critical value multiplied by the standard error. Commonly reported in survey...
- Standard Error (SE)
- The standard deviation of the sampling distribution of an estimator. For the sample mean, SE equals the population standard deviation divided by...