Confidence interval

A confidence interval is a range of values, computed from sample data, meant to estimate an unknown population quantity such as a mean, a proportion, or the difference between two groups. A "95% confidence interval" refers to the procedure that produced it: if you repeated the sampling and calculation many times, about 95% of the intervals generated that way would contain the true value. It is not correct to say there is a 95% probability that the true value lies within this one particular interval—once calculated, a specific interval either contains the true value or it does not.

The width of a confidence interval is driven mainly by sample size and the variability in the data: more data or less noise produces a narrower, more precise interval. It is typically reported alongside a point estimate and, in testing contexts, alongside a p-value.

Confidence intervals are used in A/B testing, survey reporting, and regression output because they communicate precision, not just a single number that hides how uncertain it is. A common pitfall is reading a wide interval as if it were a narrow one, or ignoring the interval entirely and reacting only to whether a result crossed the statistical significance threshold—two results with the same point estimate but very different interval widths deserve different levels of confidence in action.