What is a confidence interval?
A confidence interval is a range of plausible values for something you can’t measure directly — a population mean, a difference, an odds ratio — built from your sample. A “95% CI” comes from a method that captures the true value about 95% of the time across repeated studies. In one number it tells you both the estimate and how precise it is.
The interpretation that’s actually correct
The careful reading: “If I repeated this study many times, about 95% of the intervals I’d build would contain the true value.” The true value is fixed; it’s the interval that varies from sample to sample. In practice, people treat a single 95% CI as “the range the true value plausibly sits in” — a fair shorthand, as long as you don’t claim a literal 95% probability for this one interval.
What makes an interval wide or narrow
- Sample size — bigger sample → narrower interval (more precision). This is the big lever.
- Variability — noisier data → wider interval.
- Confidence level — 99% is wider than 95% is wider than 90%; more confidence costs precision.
A very wide interval is the data telling you it can’t pin the answer down — usually a power problem.
How it relates to the p-value
A confidence interval and a p-value are two views of the same result. For a 95% CI: if the interval for a difference excludes 0 (or a ratio excludes 1), you have p < 0.05. But the interval shows what the p-value hides — the effect size, its direction, and its precision — which is exactly why journals increasingly ask for intervals, not bare p-values.
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Frequently asked questions
What is a confidence interval in simple terms?
A range of plausible values for an unknown population quantity, built so the method captures the truth ~95% of the time.
Is there a 95% chance the true value is inside it?
Not for your specific interval, strictly — the 95% is the method’s long-run hit rate. As a shorthand for “plausible range” it’s fine.
What makes it wider or narrower?
Sample size (bigger → narrower), variability (more → wider), and confidence level (higher → wider).
How does it relate to the p-value?
If a 95% CI for a difference excludes 0, then p < 0.05 — but the interval also shows size, direction, and precision.