Confidence interval

A range of values produced by a statistical procedure designed to contain an unknown population parameter at a specified long-run frequency. Its stated confidence level describes the procedure’s repeated-sampling coverage, not the probability that one computed interval contains the parameter.

Sampling distribution: The probability distribution of a statistic across repeated samples from the same population. Confidence intervals are calibrated using how their estimates vary across hypothetical samples.
Population parameter: A numerical characteristic of a population, such as its mean, proportion, or variance. A confidence interval is constructed to cover this fixed but unknown quantity.
Credible interval: A Bayesian interval containing a specified posterior probability of a parameter, given data and a prior model. Unlike a confidence interval, it can assign posterior probability directly to the parameter lying in the interval.
Confidence interval for a mean: An interval estimate for a population arithmetic mean based on sample data and a sampling model. This common case uses the sample mean and its standard error to bound an unknown average.
Standard error: The standard deviation of a statistic’s sampling distribution, estimated from data or a model. It measures the sampling uncertainty that determines an interval’s width.
Point estimate: A single value calculated from sample data to estimate an unknown population parameter. Many intervals center on a point estimate and extend outward to represent uncertainty.
Prediction interval: An interval intended to contain a future observation with a specified probability under a statistical model. It targets a future data value, not the population parameter targeted by a confidence interval.
Confidence interval for a proportion: An interval estimate for a population proportion based on observed successes and a statistical method. It bounds an unknown prevalence or rate while accounting for sampling variability.
Critical value: A quantile of a reference distribution used to set a decision threshold or interval boundary. The selected quantile sets how many standard errors extend from the estimate.
Random sample: A sample selected according to a chance-based procedure from a population. The interval’s repeated-sampling interpretation depends on how samples are generated.

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