What is a confidence interval?

A confidence interval is a range of numbers around a study’s result that is compatible with the data.^[1][2][3][4] It reflects aspects of uncertainty about the results of a study.^[1][4]

In a clinical trial, researchers measure how an intervention changes an outcome in a sample of people. From that sample, they calculate a confidence interval: a range of values that are reasonably compatible with what they observed in those people. The width of this interval depends a lot on the number of people in the study and how much the outcome varies from person to person. Bigger studies with more participants and less variation tend to result in narrower, more precise confidence intervals, suggesting that a smaller range of values is reasonably compatible with the data.

Most clinical trials report a 95% confidence interval, written as 95% CI. In simple terms, if the same study was repeated over and over in many similar groups of people, about 95% of the calculated confidence intervals would include the true value. A narrow 95% CI suggests more precision and less uncertainty than a wide one. Importantly, it does not mean researchers are 95% “personally confident” in the result. Confidence intervals describe statistical uncertainty, not gut feeling.

Researchers often describe confidence intervals as ranges of “plausible” or “compatible” values for the true size of an effect.^[5][4] This is one reason confidence intervals are more informative than P-values by themselves. Instead of giving a yes/no answer about statistical significance, a confidence interval helps researchers evaluate the possible clinical significance of an effect.^[1][2][3][4]

Examples of interpreting confidence intervals

1. A clinically significant effect with a precise estimate of the effect: A meta-analysis of randomized controlled trials in adults over 60 with obesity, type 2 diabetes, and pre-existing cardiovascular disease found that, compared with usual care, weight loss reduced cardiovascular disease mortality with a relative risk of 0.75 and a 95% CI from 0.65 to 0.85. The relative risk of 0.75 means there was a 25% lower risk of cardiovascular death in the weight loss group. The entire confidence interval (0.65 to 0.85) is below 1 and is fairly narrow. This suggests the estimated risk reduction is precise, with low uncertainty. Overall, the results likely reflect a real mortality benefit from weight loss in a high-risk population.

2. A nonclinically significant effect despite a precise estimate of the effect: A randomized controlled trial (RCT) in people with dyslipidemia reported that the average change in LDL for a new lipid-lowering drug was –0.5 mg/dL with a narrow 95% CI of –0.1 to –1 mg/dL. The narrow confidence interval suggests a precise and statistically significant estimate of the effect, but the –0.5 mg/dL decrease is clinically irrelevant.

3. A nonclinically significant effect due to an imprecise and highly variable estimate of the effect: An RCT in people with high blood pressure reported that, compared to a placebo, a new supplement decreased blood pressure by 5 mmHg, with a 95% CI from –10 to +25 mmHg. At first glance, the average drop of 5 mmHg seems meaningful. However, the confidence interval is wide and crosses zero, ranging from a clear benefit (–10 mmHg) to possible harm (+25 mmHg). This indicates the estimated effect of the supplement is imprecise and that there is substantial uncertainty about its true effect on blood pressure.

4. A clinically significant effect despite a wide confidence interval: Another RCT in people with high blood pressure reported that, compared to a placebo, a supplement decreased blood pressure by 20 mmHg, with a 95% CI from –9 to –31 mmHg. Despite the wide confidence interval, the entire range is below zero, which suggests a statistically significant effect. Furthermore, the average decrease in blood pressure (–20 mmHg) is very large and clinically meaningful, and even the lower limit of the confidence interval (–9 mmHg) is a large and clinically important change.