What is a confidence interval used for?

A confidence interval is a statistical tool used to estimate the range within which a population parameter, such as a mean or proportion, is likely to fall with a certain level of confidence. It essentially provides an interval estimate around a sample statistic, indicating how reliable that estimate is.

When we calculate a confidence interval, we're using the data from a sample to draw conclusions about a broader population. The interval is constructed based on the sample data, and it takes into account the variability of the data, often defined by the standard error. The width of the confidence interval reflects the uncertainty around the estimate: a wider interval suggests less reliability about the estimate, while a narrower interval indicates more precision.

This is fundamentally different from measuring variability, finding correlations, or conducting hypothesis testing, which have their own specific purposes. By focusing on the estimation of reliability, confidence intervals help researchers and decision-makers understand how much trust they can place in their sample estimates when making inferences about the whole population.