What a 95% confidence interval represents
A 95% confidence interval is a range of values that are compatible with the study data, and it shows how uncertain a result is.
Remember
The 95% belongs to the method, not to one interval: if the study were repeated many times, about 95% of such intervals would contain the true value under the method's assumptions, while any one calculated interval either contains it or does not.
One study gives you one number, such as a prevalence, from its sample (the participants that study measured). Another sample would give a slightly different number. A confidence interval is a range of values that are compatible with the study data, so it shows how uncertain the estimate (the figure worked out from the sample) is.
The 95% describes the method, not one calculated interval. If the study were repeated many times on fresh samples, an interval would be calculated each time. That is repeated sampling, and about 95% of those intervals would contain the true value in the population (the group the sample was drawn from), under the method's assumptions. The true value is fixed; it is the interval that varies from sample to sample. One calculated interval either contains the true value or it does not, so it is not correct to say there is a 95% probability that the true value lies inside it.
The width of the interval tells you about precision: a wide interval means the study cannot pin the estimate down. A wider interval means a less precise estimate, often because the sample is small or events are few, and a narrower interval means a more precise one.
The interval is not a summary of the individual measurements. Their spread is described by measures such as the standard deviation (how spread out they are around the sample mean). Nor does it measure bias (systematic error from the way a study is designed or measured), and it does not give the probability that a result is due to chance.
Key facts
- What it shows
- a range of values compatible with the sample data, which quantifies the uncertainty around the estimate.
- Meaning of 95%
- about 95% of intervals from repeated samples would contain the true population value, under the method's assumptions.
- One interval
- the true value is fixed, so one calculated interval either contains it or does not.
- Width
- wider intervals mean less precision and narrower intervals mean more precision.
- What it expresses
- the uncertainty that comes from random sampling, not systematic bias.
- Not about individuals
- the interval does not describe individual patients.
Exam traps
- Saying there is a 95% probability that the true value lies inside the one interval you calculated is wrong, because the true value is fixed and the 95% describes how the method performs across repeated samples.
- A confidence interval does not hold 95% of individual patient measurements, because it describes the uncertainty in an estimate of a population value and it narrows as the sample size grows.
- The interval does not predict where future sample results will land, because it is built to capture the true population value, and later samples scatter around that true value, not around the limits of this one interval.
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