A Basic Explanation of Confidence Intervals

This article is from the U.S. Census Bureau , last revised May 4, 2017

What is a confidence interval?

A confidence interval is a range of values that describes the uncertainty surrounding an estimate. We indicate a confidence interval by its endpoints; for example, the 90% confidence interval for the number of people, of all ages, in poverty in the United States in 1995 (based on the March 1996 Current Population Survey) is "35,534,124 to 37,315,094." A confidence interval is also itself an estimate. It is made using a model of how sampling, interviewing, measuring, and modeling contribute to uncertainty about the relation between the true value of the quantity we are estimating and our estimate of that value.

How do we interpret a confidence interval?

The "90%" in the confidence interval listed above represents a level of certainty about our estimate. If we were to repeatedly make new estimates using exactly the same procedure (by drawing a new sample, conducting new interviews, calculating new estimates and new confidence intervals), the confidence intervals would contain the average of all the estimates 90% of the time. We have therefore produced a single estimate in a way that, if repeated indefinitely, would result in 90% of the confidence intervals formed containing the true value.

We can increase the expression of confidence in our estimate by widening the confidence interval. For the same estimate of the number of poor people in 1996, the 95% confidence interval is wider -- "35,363,606 to 37,485,612." The Census Bureau routinely employs 90% confidence intervals.

Why have confidence intervals?

Confidence intervals are one way to represent how "good" an estimate is; the larger a 90% confidence interval for a particular estimate, the more caution is required when using the estimate. Confidence intervals are an important reminder of the limitations of the estimates.

For a discussion on confidence intervals for the difference between two estimates, please go to General Cautions about Comparisons of Estimates.

General Cautions About Comparing Estimates

View caution statements regarding comparing SAIPE estimates with other estimates.