Core concept
- A 95% CI means: if the study were repeated infinitely many times, 95% of the calculated intervals would contain the true population value -- it is a statement about the method's long-run performance, not a 95% probability that this particular interval contains the true value
- CI width reflects precision: wider CI = smaller sample/more variability = less precise estimate; narrower CI = larger sample/more precision
- For a difference measure (RR, OR, HR, mean difference), the CI excluding the null value (1 for ratios, 0 for differences) indicates statistical significance at that confidence level -- equivalent to p<0.05 for a 95% CI
Key detail
- *Common misinterpretation to reject: "95% of the true values/observations lie within this interval" -- wrong; that describes a reference range, not a confidence interval. The CI is about the precision of one estimated parameter* (e.g. the mean, or the RR), not about spread of individual data points
- CI overlap between two groups' individual estimates does NOT automatically mean no significant difference between them -- overlapping individual CIs can still yield a significant result when the difference between the groups is tested directly; the reverse (non-overlapping CIs implying significance) is a safer but still imperfect rule of thumb
- Narrow CI entirely on one side of the null with a clinically small effect size can be statistically significant but clinically unimportant -- significance and clinical relevance are separate questions
Clinical relevance
- Trap in trial critique: a subgroup analysis with a wide, null-crossing CI ("trend towards benefit") is not evidence of an effect -- it means the study was underpowered for that subgroup, not that there is a small real effect
- When critiquing two trials with similar point estimates but different CI widths, prefer the trial with the narrower CI (from typically larger sample size) as the more precise estimate
- Reporting a point estimate without its CI hides how much uncertainty surrounds it -- always ask for the interval, not just the headline number
Correlations
- CI width is mathematically related to standard error (SE): 95% CI of a mean = point estimate +/- 1.96 x SE -- same 1.96 that defines the conventional p<0.05 threshold
- Statistical power and sample size calculations directly determine expected CI width before a study is even run
- P-value and CI are two views of the same hypothesis test -- a p-value below 0.05 and a 95% CI excluding the null value will always agree
4 of 4 sections written · drafted 2026-09-13