Confidence Intervals

A 95% confidence interval is the range that would contain the true value in 95% of repeated samples. Its width reflects precision — driven by sample size and variability.

Three effect estimates, each a point estimate (dot) with its 95% CI whisker, plotted against the vertical line of no effect (=1 for ratios). Studies A and C have intervals that exclude the null (significant); Study B’s wide interval crosses it (non-significant).

If the 95% CI excludes the null (1 for ratios, 0 for differences) the result is statistically significant. A narrow interval means a precise estimate; a wide one means uncertainty. Then ask the clinical question: are the interval’s limits meaningful?

A CI conveys significance and clinical relevance at once — is the whole interval trivial, or does it span both meaningful benefit and harm? That makes it far more informative than a bare p-value, which tells you only whether, not how much.

• 95% CI excludes the null → statistically significant
• Width = precision (narrower is better)
• Prefer CIs to bare p-values — effect size + uncertainty together

CRASH-2 (Lancet 2010) — 20,211 trauma patients with, or at risk of, significant haemorrhage, TXA vs placebo. All-cause mortality 16.0% → 14.5%, RR 0.91 (95% CI 0.85–0.97): the interval excludes 1, so the benefit is statistically significant. Statistical significance ≠ importance — always check whether the interval’s limits are clinically meaningful, not just whether it clears the null line.

• Claiming “95% of the data lie within the CI” — it describes the estimate, not the spread of observations.
• Assuming overlapping CIs automatically mean no significant difference.
• Confusing a confidence interval with a prediction interval.