rmse: Root-Mean-Squared and Relative Differences

In USGS-R/smwrStats: R functions to support statistical methods in water resources

Root-Mean-Squared and Relative Differences

Description

Computes the root-mean-squared error (RMSE) of the difference between observed values and the predicted values or the RMSE or relative percent differences (RPD) between samples and duplicates.

Usage

rmse(x, ...)

## Default S3 method:
rmse(x, y, ...)

## S3 method for class 'lm'
rmse(x, ...)

rpd(x, y, plotit = FALSE)

Arguments

x	either a random vector an object for which a method exists.
y	duplicate samples paired with x.
plotit	logical, if TRUE, then create a Bland-Altman mean-difference plot (banld and Altman, 1986); otherwise no plot is created.
...	arguments to be passed to or from methods.

Value

For the rmse functions, a single value representing the estimated RMSE. For rpd, the relative percent differences for each paired sample and duplicate.

Note

The definition for the RMSE of paired water-quality duplicates is

RMSE = sqrt(sum of squared differences/2 times the number of duplicates)

The definition for RPD for paired water-quality duplicates is

RPD = abs(x - y)/(x + y)/2 * 100

Other disciplines may use different equations.

References

Bland J.M. and Altman D.G., 1986 Statistical methods for assessing agreement between two methods of clinical measurement: Lancet, i, p. 307–310.

Clesceri, L.S., Greenberg, A.E., and Eaton, A.D., 1998, Standard methods for the examination of water and wastewater, 20th edition: Baltimore, Md, United Book Press, Inc., 1162 p.

Harvey, D., undated, Analytical chemistry 2.0: Analytical Sciences Digital Library: online at URL: http://www.asdlib.org/onlineArticles/ecourseware/Analytical

Helsel, D.R., and Hirsch, R.M., 2002, Statistical methods in water resources: U.S. Geological Survey Techniques of Water-Resources Investigations, book 4, chap. A3, 522 p.

Examples

# Example 15.2 from Harvey.
dupX1 <- c(160, 196, 207, 185, 172, 133)
dupX2 <- c(147, 202, 196, 193, 188, 119)
rmse(dupX1, dupX2)
rpd(dupX1, dupX2)

USGS-R/smwrStats documentation built on Oct. 11, 2022, 6:15 a.m.