Confidence interval
A confidence interval is a range estimate that shows uncertainty around a sample-based statistic.
What a confidence interval is
A confidence interval is an interval estimate for an unknown population parameter, such as a mean, proportion, risk difference, or treatment effect. Instead of reporting only a single sample estimate, it gives a range of values that are compatible with the data and the statistical method used.
Confidence level
The confidence level describes the long-run behavior of the procedure. If a valid 95 percent confidence interval method were repeated many times on new random samples from the same population, about 95 percent of those intervals would contain the true parameter. The confidence level is about the method, not magic certainty about one finished interval.
Point estimate and margin of error
Many confidence intervals are built around a point estimate, such as a sample mean or sample proportion. The margin of error is the distance from that estimate to each end of the interval when the interval is symmetric. It depends on the variability in the data, sample size, chosen confidence level, and statistical assumptions.
Reading the width
Interval width is often as important as the center. A wide interval may include values with very different practical meanings, which signals imprecision. A narrow interval can make interpretation easier, but only if the sampling, measurement, and model assumptions behind it are reasonable.
Relation to p-values
Confidence intervals and p-values are connected but answer different questions. A p-value summarizes how surprising the data would be under a null model. A confidence interval shows a range of effect sizes or parameter values, which helps readers judge both direction and magnitude.
Common interpretations
A 95 percent confidence interval should not be read as saying there is a 95 percent probability that the fixed true value lies inside this particular interval. In frequentist statistics, the parameter is treated as fixed and the interval is random because it came from a random sample. Bayesian credible intervals use a different interpretation.
Limits and assumptions
A confidence interval can be misleading when the sample is biased, the model is wrong, the data were repeatedly analyzed until a pleasing interval appeared, or the formula is used outside its valid conditions. Good reporting explains the design, sample, method, and any adjustments for complex data or multiple comparisons.
Why it matters
Confidence intervals push research reporting beyond yes-or-no significance. They show how precise an estimate is, whether plausible effects are practically small or large, and how much uncertainty remains after collecting the data.