What Is a Confidence Interval?

A confidence interval (CI) gives a range of values for an effect or quantity that are reasonably compatible with the data, at a stated confidence level (often 95%). It shows both the size and the precision of an estimate, which a p-value alone does not.

Interpretation

A 95% CI is constructed so that, if the study were repeated many times and an interval were calculated each time with the same method, about 95% of those intervals would contain the true value (assuming the model is correct). Informally, values inside the interval are reasonably compatible with the data and values outside it are less so. It is not accurate to say "there is a 95% probability that this interval contains the true value" for one calculated interval, although this phrase is common in practice.

What the width tells you

• Narrow intervals suggest high precision; wide intervals suggest uncertainty.
• Width shrinks with larger samples and lower variability.

Relation to significance

For a ratio measure, if the 95% CI excludes 1, the result is statistically significant at the 5% level; for a difference, if it excludes 0. But the interval gives more: you can judge whether the plausible range includes clinically important values.

Illustrative example

Invented for teaching. A trial reports a mean difference in systolic blood pressure of −6 mm Hg (95% CI −12 to 0). The interval includes values from a substantial reduction to no effect, so the study suggests benefit but is imprecise. A second trial reports −6 mm Hg (95% CI −7 to −5), a very precise estimate with the same size of effect.

How to use in reading

1. Check whether the interval includes the null value.
2. Ask whether both ends of the interval would be clinically important.
3. Note how wide it is.

Common pitfalls

• Treating the interval as the range of individual patient values.
• Concluding "no effect" because the interval includes zero when it also includes important effects.

Key takeaways

• CI = estimate plus plausible range.
• Judge both direction and clinical importance of the ends.

This page is general educational information about research methods. It is not medical, legal or regulatory advice; follow your institution's ethics board and your target journal's instructions.