Statistics for Researchers › Module 2: Samples and uncertainty
Confidence intervals
Lesson 3 of 3 · 2 min
A confidence interval (CI) gives a range of plausible values for the true number, instead of a single guess.
"The new method improves accuracy by 3 points, 95% CI 1 to 5" means: our best estimate is 3, and values between 1 and 5 are consistent with the data.
What "95%" really means
If you repeated the whole study many times and built a 95% interval each time, about 95% of those intervals would contain the true value. It is a statement about the method, not a 95% chance that this particular interval is right. In practice, read it as "the range of values the data supports".
For large samples, a 95% CI is roughly the estimate ± 2 standard errors.
Why CIs beat a lone p-value
A CI shows two things at once:
- Size: how big the effect plausibly is.
- Precision: how wide the range is.
| Result | What it tells you |
|---|---|
| +3 points, 95% CI 2.5 to 3.5 | A clear, precisely measured gain |
| +3 points, 95% CI −4 to +10 | Could be a gain, nothing, or a loss: we don't know |
- +3 points, 95% CI 2.5 to 3.5
- What it tells you: A clear, precisely measured gain
- +3 points, 95% CI −4 to +10
- What it tells you: Could be a gain, nothing, or a loss: we don't know
Both might be reported as "a 3-point improvement". Only the interval reveals the difference. This is why many statisticians, including Geoff Cumming, argue for reporting estimates and CIs as the main result.
RememberReport the estimate with its 95% CI. A wide interval is honest uncertainty, not a failure.