Statistics Definitions > Relative Precision

## What is Relative Precision?

“Relative Precision”(RP) is one of those catch all terms that can mean slightly different things depending on where you’re using it. For example, the coefficient of variation is a type of RP used to compare results from two tests or surveys, while in more general terms, RP is a way to show **uncertainty as a fraction of a quantity**. It is the ratio of a measurement’s precision and the measurement itself. Let’s say that t is a measurement and s_{t} is the standard deviation of the measurement. The **relative precision formula **is: s_{t}/t. It usually given as a ratio (e.g. 5/8), or as a percentage.

Relative precision can also be used to show a confidence interval for a measurement. For example, if the RP is 10% and your measurement is 220 degrees, then the confidence interval is 220 degrees ±22 degrees. Confidence levels for precision are usually reported with a confidence level. In general, there is a tradeoff between confidence levels and precision. The higher the confidence level, the wider the confidence interval, and the lower the precision.

## Relative Precision in Sampling

Relative precision in sampling refers to the **ratio of the error variances of two different sample designs which have the same sampling unit and sample size**. When used in this way, RP is also called *relative efficiency*. If you use simple random sampling to find the mean of a large population, relative precision and relative efficiency are equal. In other cases, they may not be equal.

## Coefficient of Variation

The coefficient of variation is one of the more common measurements of RP, and is the ratio of the standard deviation over the mean of the measurements. For example, the expression “The standard deviation is 15% of the mean” is a coefficient of variation.

**Reference:
**A Dictionary of Statistical Terms, 5th edition, prepared for the International Statistical Institute by F.H.C. Marriott. Published for the International Statistical Institute by Longman Scientific and Technical.

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