GlossaryStatistics and interpretation
Confidence interval
A confidence interval is a range calculated around an estimate using a method designed to capture the unknown population value at a stated long-run rate.
A confidence interval is a range calculated around an estimate using a method designed to capture the unknown population value at a stated long-run rate. It expresses uncertainty from estimation under the method's assumptions. It does not guarantee that the particular interval contains the true value or account for every possible data error.
Reading the range
The NIST statistical handbook explains a 95% confidence level in terms of repeated sampling: over many comparable samples, about 95% of intervals produced by the method would contain the population value.
The estimate remains the reported central value; the endpoints show uncertainty under the method used. Wider intervals generally communicate less precision. The confidence level, sample design, and estimation method belong with the range, especially when estimates come from complex surveys rather than simple random samples.
Example
Hypothetical example: A survey estimates that 30% of residents experienced a specified problem during the past year, with a 95% confidence interval from 26% to 34%.
The interval describes uncertainty around the estimated population percentage. It does not mean that 95% of residents fall between 26% and 34%, because residents are not being measured on that percentage scale. It also does not mean the next year's percentage is predicted to lie in that range.
Common confusion
A margin of error is often the distance from an estimate to an interval endpoint when the interval is symmetric. It is not the same thing as the entire interval's width. In the example, the margin is four percentage points and the width is eight.
A prediction interval concerns possible future or individual observations. A confidence interval concerns an estimated population quantity.
Limits of inference
The interval does not automatically cover underreporting, biased questions, incorrect records, or a poorly matched population. When comparing two estimates, use an appropriate comparison method rather than deciding significance solely from whether their separate intervals overlap. The source's methodology should identify what uncertainty was calculated.