The frequentist interval that would contain the true value in a stated fraction of repeated experiments.A confidence interval is a range of values, computed from sample data, that is intended to contain the true population parameter (like a mean or proportion) with a certain level of confidence, typically 95%. The key frequentist interpretation is: if you repeated the experiment many times and computed a confidence interval each time, about 95% of those intervals would contain the true value. It is not a statement about the probability that the true value lies within any particular interval — that probability is either 0 or 1, since the true value is fixed.
The concept was introduced by Jerzy Neyman in 1937, building on earlier work by Ronald Fisher on fiducial inference, and it became a standard tool in statistics thereafter.
To construct a confidence interval, you estimate the parameter from the sample (e.g., the sample mean) and then add and subtract a margin of error. The margin of error is the product of a critical value from a relevant distribution (like the t-distribution) and the standard error of the estimate. The critical value is chosen so that the interval captures the central 95% of the sampling distribution. The result is an interval like '5.2 ± 0.8', meaning you are 95% confident the true mean lies between 4.4 and 6.0.
Confidence intervals are used in virtually every quantitative study to report the precision of estimates — from opinion polls to clinical trial outcomes — and to assess whether effects are practically meaningful.
A 95% confidence interval does not mean there is a 95% chance the true value is in the interval; that misinterpretation is so common it has its own name: the 'confidence interval fallacy'.
