# Confidence interval

A confidence interval is a range of values, calculated from sample data, that is built by a procedure designed to capture the true population value in a fixed proportion of repeated studies. That proportion is the confidence level, conventionally 95%. For a simple estimate the interval runs from the point estimate minus about 1.96 standard errors to the point estimate plus about 1.96 standard errors. Width falls with sample size: quadrupling the sample halves the interval. Studies report it as 'hazard ratio 0.82, 95% CI 0.71 to 0.94'. The correct frequentist reading is a statement about the method, not about the one interval on the page. If the study were repeated many times under identical conditions, 95% of the intervals produced this way would contain the true value. The interval in front of you either contains it or does not. The common misreading is that there is a 95% probability the true value lies between 0.71 and 0.94. That describes a Bayesian credible interval and requires a prior distribution. It persists because it is the answer readers actually want and because the word confidence sounds like probability. Surveys of researchers and students find the error is close to universal. In longevity and nutrition research, small trials produce wide intervals spanning 1.0. These are often written up as showing no effect when they are simply uninformative.

## Sources

- Gardner MJ, Altman DG. (1986). Confidence intervals rather than P values: estimation rather than hypothesis testing. BMJ. https://doi.org/10.1136/bmj.292.6522.746
- Greenland S, Senn SJ, Rothman KJ, et al.. (2016). Statistical tests, P values, confidence intervals, and power: a guide to misinterpretations. European Journal of Epidemiology. https://doi.org/10.1007/s10654-016-0149-3
- Hoekstra R, Morey RD, Rouder JN, et al.. (2014). Robust misinterpretation of confidence intervals. Psychonomic Bulletin & Review. https://doi.org/10.3758/s13423-013-0572-3

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_Canonical: https://longevity-germany.com/en/glossary/confidence-interval · Part of Longevity Cities · Updated 2026-08-25_