Confidence Interval

A confidence interval is produced by a procedure with a specified repeated-sampling coverage rate under its assumptions. A ninety-five-percent method aims to cover the fixed parameter in about ninety-five percent of repeated applications.

A frequentist confidence interval comes from a procedure designed to cover a fixed parameter at a stated rate over repeated sampling under its assumptions. The probability statement concerns the procedure before the sample is observed. It is not automatically a posterior probability that the fixed parameter lies inside this particular realized interval.

Width measures a form of sampling precision, not protection against bias or model error. A narrow interval can be centered on the wrong quantity when sampling is selective or assumptions fail. An interval for a population mean also differs from a prediction interval for one future observation, which generally includes additional variability.

When to use it

When analyzing data; when building predictive models; when evaluating statistical claims; when quantifying uncertainty.

How it can help

Identify the parameter and method, interpret sampling coverage correctly, compare precision with practical needs, and inspect bias and model assumptions.