The Core Question Each Interval Answers
All three intervals are computed from sample data, but they express uncertainty about different things:
Confidence Interval
Captures uncertainty about the mean of the population. A 95% CI means that if you repeated the experiment many times, 95% of the computed intervals would contain the true population mean. The CI becomes narrower as you collect more data, because your estimate of the mean improves.
Prediction Interval
Captures where a single future observation is expected to fall. A 95% PI means that 95% of new individual measurements from the same population will land within the interval. The PI is always wider than the CI because it incorporates both the uncertainty in the mean and the natural variability of individual observations. Even with an infinite sample, the PI does not collapse to a point — individual variation remains.
Tolerance Interval
Covers a specified proportion of the population with a specified confidence. A 95%/99% tolerance interval means you are 95% confident that at least 99% of the population falls within the interval. Tolerance intervals are common in quality control and manufacturing, where you need to certify that a product spec covers nearly all units produced.
Comparison Table
| Interval | Answers | Captures | Width vs. N |
|---|---|---|---|
| Confidence Interval (CI) | Where is the true population mean? | The mean of the population | Larger samples → narrower CI |
| Prediction Interval (PI) | Where will the next single observation fall? | A single future observation | Always wider than CI; N has less impact |
| Tolerance Interval (TI) | What range covers at least X% of the population? | A specified proportion of the population | Wider as coverage proportion increases |
The Most Common Mistake
Mistaking a CI for a PI
The most common error is interpreting a confidence interval as if it tells you where individual measurements will fall. It does not. A CI tells you about the mean; a PI tells you about individuals. If you say "our treatment gives a blood pressure of 120 mmHg (95% CI: 118-122)" and a colleague assumes that means 95% of patients will have BP between 118 and 122 — that is an incorrect interpretation. The prediction interval for individual patients would be much wider.