Confidence Intervals

CONFIDENCE INTERVALS

Point estimates can be used to obtain our best determination of a single value that operates as a parameter. However, point estimates by themselves do not express the uncertainty in the estimate (i.e., the variability in its sampling distribution). However, under certain statistical assumptions the sampling distribution of the estimate can be determined (e.g., for the sample mean when the population distribution is normal with known variance). In other circumstances, the sampling distribution can be approximated (e.g., for the sample mean under the assumptions needed for the central limit theorem to hold along with the standard deviation estimated from a sample). This information enables us to quantify the uncertainty in a confidence interval. Confidence intervals express the probability that a prescribed interval will contain the true parameter.