In statistics, a relative standard error, or RSE, is equal to the standard error of a survey estimate divided by the survey estimate and then multiplied by 100. The number is multiplied by 100, so it can be expressed as a percentage. The RSE does not necessarily represent any new information beyond the standard error, but it might be a superior method of presenting statistical confidence.

Survey Estimate and Standard Error

Surveys and standard errors are crucial parts of probability theory and statistics. Statisticians use standard errors to construct confidence intervals from their surveyed data. Confidence intervals are important for determining the validity of empirical tests and research.

In layman's terms, the standard error of a data sample is a measurement of the likely difference between the sample and the entire population. For example, a study involving 10,000 cigarette-smoking adults may generate slightly different statistical results than if every possible cigarette-smoking adult was surveyed.

Smaller sample errors are indicative of more reliable results. The central limit theorem in inferential statistics suggests that large samples tend to have approximately normal distributions and low sample errors.

Standard Deviation and Standard Error

The standard deviation of a data set is used to express the concentration of survey results. Less variety in the data results in a lower standard deviation. More variety is likely to result in a higher standard deviation.

The standard error is sometimes confused with standard deviation. The standard error actually refers to the standard deviation of the mean. Standard deviation refers to the variability inside any given sample, while a standard error is the variability of the sampling distribution itself.

Relative Standard Error

Relative Standard Error = (Standard Error / Estimate) x 100
Relative Standard Error Formula Example.  Investopedia

The standard error is an absolute gauge between the sample survey and the total population. The relative standard error shows if the standard error is large relative to the results; large relative standard errors suggest the results are not significant. The formula for relative standard error is (standard error/estimate) x 100.