KONSİLWhat is a confidence interval?
A confidence interval is an interval estimate of an effect. A 95% interval means that across many repetitions of the study about 95% of such intervals would cover the true value; it does not mean the one interval obtained has a 95% chance of containing it.
A confidence interval shows the uncertainty around a point estimate: with a narrow interval the effect is known precisely, with a wide one it is not. According to the Cochrane Handbook (chapter 15) the width depends on the sample size, for continuous outcomes also on the standard deviation of the measurements, and for binary outcomes on how frequent the event is; larger studies tend to give narrower intervals.
Schumi and Wittes (2011) and Greenland et al. (2016) give the same strict reading: imagine the study repeated an unlimited number of times, each time with a new 95% interval; 95% of those intervals would include the true effect. According to Greenland et al. this coverage probability belongs to a long sequence of intervals computed from valid models, not to any single interval. The Cochrane Handbook calls the reading ‘the true effect lies in this interval with 95% certainty’ a loose interpretation, useful as a rough guide.
Relation to p-values: according to Greenland et al., a 95% confidence interval corresponds to the set of effect sizes whose test gives P > 0.05. Altman and Bland (2011) state that confidence intervals are usually considered more informative than P values. The Cochrane Handbook asks review authors to give the confidence interval alongside the precise P value rather than labelling results ‘statistically significant’.
Example
In a hypothetical study the mean blood pressure difference is 4 mmHg with a 95% confidence interval of 1 to 7 mmHg. By the definition in Greenland et al., an interval that excludes zero means the two-sided P value of the same comparison is below 0.05; the interval also shows that the effect may be as small as 1 mmHg or as large as 7 mmHg.
A point to watch
Greenland et al. (2016) list the reading ‘a specific 95% confidence interval has a 95% chance of containing the true effect’ among the common misinterpretations: an observed interval either contains the true effect or does not, and the 95% describes the long-run coverage of intervals computed across very many studies. According to the same source, overlapping confidence intervals do not show that a difference is non-significant.
Related terms
Guides and tools
Sources
- Statistical tests, P values, confidence intervals, and power: a guide to misinterpretations — European Journal of Epidemiology (Springer), 2016
- Cochrane Handbook for Systematic Reviews of Interventions, Chapter 15: Interpreting results and drawing conclusions — Cochrane, 2024
- How to obtain the confidence interval from a P value — BMJ, 2011
- Through the looking glass: understanding non-inferiority — Trials (BioMed Central), 2011