Relative Variance

Statistics Definitions > Relative Variance

What is the Relative Variance?

The relative variance (RV) is a measure of error, or how much the “noise” of a data point or set of data points can vary. RV doesn’t have a universal definition, and it isn’t used very often in statistics except in very informal terms. Different definitions include (in no particular order):

Definition 1

The relative variance is the variance, divided by the absolute value of the mean (s2/|x̄|). You can also multiply the result by 100 to get the percent RV. Note: the two terms relative variance and percent relative variance are sometimes used interchangeably.

Definition 2

This one makes the most sense to me personally, although I’m sure other opinions differ. Hermance (2013) defines the RV in terms of rainfall. The variance of rainfall at a certain station is composed of three different variances. The RV is used to “…define the effect that the variability of rainfall for a given month has on the variability of the rainfall over the entire season for the station.” It’s a relatively simple definition, with this formula (where sd = standard deviation):

Hermance definition for Relative variance for august rainfall, based on three months formula
Relative variance for august rainfall, based on three months (July, August, September).

Definition 3

I found a single reference to another (very similar) formula, in a U.S. Department of Commerce publication, which defined RV as “the variance divided by the square of the estimate.”
Relative variance divided by the square of the estimate formula
The last part might be a lesson in how many definitions for can become confusing. It reads that the “…square root of the RV is defined as the coefficient of variation“.

  • By this definition, the square of the coefficient of variation must equal the RV squared.
  • The coefficient of variation is defined as the standard deviation divided by the mean.
  • Therefore, the variance divided by the square of the estimate — squared, should equal the standard deviation divided by the mean

    • .

This doesn’t equate, so be careful when you’re using the RV as a calculation.

I’ve also seen RV calculated as:

  • The square root of the variance divided by the mean:
  • The standard deviation divided by the mean.
  • A constant multiplied by a diameter, divided by a weight (here).

In sum, there isn’t a standard formula, so be very careful if using this statistic — you may end up confusing your readership.

References:
Hermance, J. (2013). Historical Variability of Rainfall in the African East Sahel of Sudan: Implications for Development. Springer Science & Business Media.
Poole, C. et. al. (2001). Relative thin-layer chromatography, a practical survey. P. 318.
Relative Var. Dataplot reference manual. September 3, 1996.
U.S. Dept. of Commerce. (1968). Agrostan: A Case Study for the 1970 World Census of Agriculture, Volume 3
willhelm-Welmer, F. (2012). Statistical Evaluations in Exploration for Mineral Deposits. Springer Science & Business Media.


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