A 95 percent confidence interval is built so that, over many repeated samples, 95 percent of such intervals would contain the true parameter. For a mean it is roughly the sample mean plus or minus 2 standard errors, and it narrows with the square root of the sample size. A difference whose interval excludes zero is significant at the matching alpha, and the interval's width shows how precisely the effect is pinned down.
Mean shift is 1.8 nm, 95 percent confidence interval 0.4 to 3.2. It's real, but we don't know yet if it's small or big.
Report the interval, not just the p-value: it shows whether the effect is real and how big it could plausibly be.
Also heard as
- CI
- confidence limits
- confidence bounds
Do not mix it up with
- Tolerance interval: A confidence interval brackets a parameter such as the mean; a tolerance interval brackets a stated share of the individual values.
Related terms
Tolerance interval
Range expected to contain a stated share of all individual values in a population, at a stated confidence.
p-value
Probability of seeing a result at least this extreme if there were truly no effect, used to judge statistical significance.
Standard deviation
Typical distance of individual values from their mean, the basic measure of spread, written as sigma or s.
Significant
Describes a result unlikely to have come from chance alone at a stated risk level, which is not the same as important.