Statistics · BEGINNER LESSON
Confidence interval
A confidence interval (CI) is a range of plausible values for an estimated quantity, such as an effect size or population mean. It is used to describe both the estimate itself and how much uncertainty surrounds it.
What it is and what is measured
A confidence interval is built from a point estimate, which is the single best estimate from the sample, plus and minus a margin of error. The result is a lower and upper limit that shows a range of values considered plausible for the true quantity in the population. In this literature, CIs are used to describe the magnitude of an effect and the uncertainty around that magnitude, not to prove a hypothesis true or false. [sourceIndexes: 0,1,2]
[1] Veterinarians' brief guide to confidence intervals, standardized ... [2] pmc.ncbi.nlm.nih.gov · articles · PMC12834938Exploring the proper use of p-values and confidence intervals ... [3] A Primer on Large-Sample Statistical Inference for Epidemiologists
How it works
A common 95% CI means that if the study and estimation process were repeated many times, about 95% of the resulting intervals would contain the true value. The width of the interval is strongly influenced by sample size and variability: small samples and highly variable data produce wider intervals, while larger and less variable samples usually produce narrower ones. Statistically, the interval is often calculated from the point estimate and a standard error, using a critical value from a reference distribution. [sourceIndexes: 0,2]
[1] Veterinarians' brief guide to confidence intervals, standardized ... [3] A Primer on Large-Sample Statistical Inference for Epidemiologists
How to read it
A narrow CI suggests more precision; a wide CI suggests more uncertainty. Some authors also describe CIs as compatibility intervals, meaning they show which parameter values fit the observed data better or worse. A CI should not be treated as a simple inside-versus-outside test for deciding whether an effect exists, because the meaning depends on the chosen confidence level and the statistical model. [sourceIndexes: 1,2]
[2] pmc.ncbi.nlm.nih.gov · articles · PMC12834938Exploring the proper use of p-values and confidence intervals ... [3] A Primer on Large-Sample Statistical Inference for Epidemiologists
Limits and cautions
CIs reflect random error and sampling variability, but they do not protect against systematic error, also called bias. A large study can still have a misleadingly narrow CI if the study design or measurements are flawed. Also, approximate CIs rely on assumptions and may be less reliable with small samples; bootstrap CIs also have limits when the sample is small. [sourceIndexes: 1,2]
[2] pmc.ncbi.nlm.nih.gov · articles · PMC12834938Exploring the proper use of p-values and confidence intervals ... [3] A Primer on Large-Sample Statistical Inference for Epidemiologists
SEE THE IDEA
How a confidence interval is formed and interpreted
Observed measurements collected from a sample
Single best estimate calculated from the sample
Amount added and subtracted to reflect uncertainty
Lower and upper limits around the estimate
Shows plausible values and precision, not proof
Sample data lead to a point estimate; uncertainty is added as a margin of error to form the confidence interval, which is then interpreted as a range of plausible values.
A CI summarizes an estimate and its uncertainty, but it does not eliminate bias or other study limitations.
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Sources and further reading
This general lesson was generated from public source material. It explains a concept; it does not interpret a private paper or provide medical advice.