What Is a Relative Standard Error (RSE)?
In statistics, relative standard error (RSE) reflects the precision and reliability of estimates. Estimates refer to conclusions drawn about a population, based on information obtained from asample of that population.
An RSE is equal to the standard error of a survey estimate divided by the survey estimate and then multiplied by 100 for a resulting 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.
Key Takeaways
- Relative standard error is used in probability theory and statistics.
- It is a view of standard error relative to a survey estimate.
- Standard error is a measurement of the amount that a survey may deviate from the overall population from which samples can be drawn.
- Relative standard error provides a different view of the data, not necessarily any new information.
- A large RSE indicates that an estimate is unreliable.
Understanding Relative Standard Error (RSE)
RSE is the standard error expressed as a fraction of the estimate and is usually displayed as a percentage.
Standard error measures how much a survey estimate is likely to deviate from all possible samples (or, the actual population). It is expressed as a number.
Estimates with an RSE of 25% or greater are subject to high sampling error and should be used with caution. In general, those with high RSEs are considered unreliable. Smaller RSEs indicate greater certainty and therefore reliability of results.
Relative Standard Error Formula
The relative standard error indicates whether the standard error is large relative to the results of the sample survey. Large relative standard errors suggest the results are not significant.
The formula for relative standard error is:
RelativeStandardError=EstimateStandardError×100where:StandardError=standarddeviationofthemeansampleEstimate=meanofthesample
When conducting research, one sample can provide a result that may differ from those obtained from other samples. Therefore, it's important to establish the sampling errors related to different samples.
Survey Estimate and Standard Error
In layman's terms, the standard error of a data sample is a measurement of the likely difference between a particular sample and the entire sample 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.
Confidence Intervals
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. The reliability of estimates can also be assessed in terms of a confidence interval.
A confidence interval is a type ofinterval estimate, computed from the statistics of the observed data, that might contain the true value of an unknownpopulation parameter.
Confidence intervals represent the range in which the population value is likely to lie. They are constructed using the estimate of the population value and its associated standard error.
For example, there is approximately a 95% chance (i.e., 19 chances in 20) that the population value lies within two standard errors of the estimates, so the 95% confidence interval is equal to the estimate plus or minus two standard errors.
Smaller sample errors imply 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 vs. 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 the standard deviation. The standard error actually refers to the standard deviation of the mean. Put another way, standard deviation refers to the variability inside any given sample, while a standard error is the variability of the sampling distribution itself.
Does Relative Standard Error Matter?
Yes, in that it relates directly to the standard error and provides a view of the scale of the standard error.
Which Is Better, A Large or Small RSE?
A large RSE is considered unreliable and conveys lack of confidence that a sample estimate reflects the actual population. A smaller RSE is seen as more precise and thus is preferred.
What Is Relative Standard Error in Simple Terms?
Relative standard error is simply the standard error displayed as a proportion of the overall survey estimate. Divide the standard error by the estimate and multiply by 100 to get the RSE.
The Bottom Line
Relative standard error can be used to present a standard error as a proportion of an estimate. It can quickly reveal for statisticians whether the results of a sample survey are useful or should be disregarded.
