Confidence Interval

Definition

A confidence interval is a range of values, computed from sample data, that is expected to contain the true population parameter with a specified probability (the confidence level). For example, a 95% confidence interval means that if the study were repeated many times, approximately 95% of the calculated intervals would contain the true parameter.

Why It Matters

Confidence intervals are more informative than p-values because they quantify both the magnitude of an effect and the precision of the estimate. A narrow interval around a large effect suggests a reliable finding, whereas a wide interval indicates uncertainty that may require a larger sample. Reporting confidence intervals is now recommended by leading scientific journals and the American Statistical Association as best practice.

Example

A study reports that a new drug reduces blood pressure by an average of 15 mmHg, with a 95% confidence interval of [10, 20]. This tells you not only that the effect is statistically significant, but also that the true effect in the population is likely to be between 10 and 20 mmHg. If the interval had been [-2, 32], you would conclude that the data are compatible with no effect at all.

Related Terms

• P-Value
• Standard Error (confidence intervals are built around the point estimate plus or minus a margin of error based on the standard error)
• Effect Size
• Statistical Significance

Software Notes

• SPSS: Most procedures (e.g., Descriptive Statistics > Explore) offer a "Confidence Interval for Mean" option. In regression, look under Statistics > Confidence Intervals.
• R: t.test(x) returns a confidence interval automatically. For regression: confint(model). For proportions: prop.test(x, n).
• Stata: ci means varname or ci proportions varname. In regression: regress y x followed by lincom x for specific contrasts with CIs.