Table of Contents
What Is Relative Standard Error?
The Relative Standard Error (RSE) is a measure of the reliability of a survey statistic. It is the standard error expressed as a fraction (or percentage) of the estimate. RSE is widely used by government statistical agencies such as the U.S. Census Bureau and the Bureau of Labor Statistics to indicate the quality of published estimates.
When the RSE is small, the estimate is considered more reliable. Estimates with an RSE above 25% are generally considered unreliable and may be suppressed or flagged in official publications. RSE below 5% indicates a highly reliable estimate.
RSE Formula
Where s is the sample standard deviation and n is the sample size. The RSE thus combines information about both the variability of the data and the sample size.
Interpreting RSE
| RSE Range | Reliability | Action |
|---|---|---|
| < 5% | Very reliable | Publish without qualification |
| 5% - 15% | Reliable | Publish with normal caveats |
| 15% - 25% | Marginal | Use with caution |
| 25% - 50% | Unreliable | Flag or suppress |
| > 50% | Very unreliable | Do not publish |
Applications in Survey Statistics
- Census data: RSE helps users assess the quality of American Community Survey estimates at different geographic levels.
- Economic surveys: Business surveys use RSE to determine whether industry-level estimates are publishable.
- Health surveys: NHANES and similar health surveys report RSE alongside prevalence estimates.
- Labor statistics: Employment and wage estimates are accompanied by RSE to guide interpretation.
Frequently Asked Questions
How is RSE different from RSD?
RSE uses the standard error (SE = s/sqrt(n)) in the numerator, while RSD uses the standard deviation (s) directly. RSE accounts for sample size, making it appropriate for survey estimates. RSD measures data variability regardless of sample size and is used in analytical chemistry and quality control.
How can I reduce the RSE of a survey estimate?
Increasing the sample size is the most direct way to reduce RSE, since the standard error decreases with the square root of n. Stratified sampling, better questionnaire design, and reducing non-response can also help by lowering the standard deviation of responses.