CoefVar {DescTools}  R Documentation 
Coefficient of Variation
Description
Calculates the coefficient of variation and its confidence limits using various methods.
Usage
CoefVar(x, ...)
## S3 method for class 'lm'
CoefVar(x, unbiased = FALSE, na.rm = FALSE, ...)
## S3 method for class 'aov'
CoefVar(x, unbiased = FALSE, na.rm = FALSE, ...)
## Default S3 method:
CoefVar(x, weights = NULL, unbiased = FALSE,
na.rm = FALSE, ...)
CoefVarCI(K, n, conf.level = 0.95,
sides = c("two.sided", "left", "right"),
method = c("nct","vangel","mckay","verrill","naive"))
Arguments
x 
a (nonempty) numeric vector of data values. 
weights 
a numerical vector of weights the same length as 
unbiased 
logical value determining, if a bias correction should be used (see. details). Default is FALSE. 
K 
the coefficient of variation as calculated by 
n 
the number of observations used for calculating the coefficient of variation. 
conf.level 
confidence level of the interval. Defaults to 0.95. 
sides 
a character string specifying the side of the confidence interval, must be one of 
method 
character string specifing the method to use for calculating the confidence intervals, can be one out of:

na.rm 
logical. Should missing values be removed? Defaults to FALSE. 
... 
further arguments (not used here). 
Details
In order for the coefficient of variation to be an unbiased estimate of the true population value, the coefficient of variation is corrected as:
CV_{korr} = CV \cdot \left( 1  \frac{1}{4\cdot(n1)} + \frac{1}{n} \cdot CV^2 + \frac{1}{2 \cdot (n1)^2} \right)
For determining
the confidence intervals
for the coefficient of variation a number of methods have been proposed. CoefVarCI()
currently supports five different methods.
The details for the methods are given in the specific references.
The "naive" method
is based on dividing the standard confidence limit for the standard deviation by the sample mean.
McKay's
approximation is asymptotically exact as n goes to infinity. McKay recommends this approximation only if the coefficient of variation is less than 0.33. Note that if the coefficient of variation is greater than 0.33, either the normality of the data is suspect or the probability of negative values in the data is nonneglible. In this case, McKay's approximation may not be valid. Also, it is generally recommended that the sample size should be at least 10 before using McKay's approximation.
Vangel's modified McKay method
is more accurate than the McKay in most cases, particilarly for small samples.. According to Vangel, the unmodified McKay is only more accurate when both the coefficient of variation and alpha are large. However, if the coefficient of variation is large, then this implies either that the data contains negative values or the data does not follow a normal distribution. In this case, neither the McKay or the modified McKay should be used.
In general, the Vangel's modified McKay method is recommended over the McKay method. It generally provides good approximations as long as the data is approximately normal and the coefficient of variation is less than 0.33. This is the default method.
See also: https://www.itl.nist.gov/div898/software/dataplot/refman1/auxillar/coefvacl.htm
nct
uses the noncentral tdistribution to calculate the confidence intervals. See Smithson (2003).
Value
if no confidence intervals are requested:
the estimate as numeric value (without any name)
else a named numeric vector with 3 elements
est 
estimate 
lwr.ci 
lower confidence interval 
upr.ci 
upper confidence interval 
Author(s)
Andri Signorell <andri@signorell.net>,
Michael Smithson <michael.smithson@anu.edu.au> (noncentralt)
References
McKay, A. T. (1932). Distribution of the coefficient of variation and the extended t distribution, Journal of the Royal Statistical Society, 95, 695–698.
Johnson, B. L., Welch, B. L. (1940). Applications of the noncentral tdistribution. Biometrika, 31, 362–389.
Mark Vangel (1996) Confidence Intervals for a Normal Coefficient of Variation, American Statistician, Vol. 15, No. 1, pp. 2126.
Kelley, K. (2007). Sample size planning for the coefcient of variation from the accuracy in parameter estimation approach. Behavior Research Methods, 39 (4), 755766
Kelley, K. (2007). Constructing confidence intervals for standardized effect sizes: Theory, application, and implementation. Journal of Statistical Software, 20 (8), 124
Smithson, M.J. (2003) Confidence Intervals, Quantitative Applications in the Social Sciences Series, No. 140. Thousand Oaks, CA: Sage. pp. 3941
Steve Verrill (2003) Confidence Bounds for Normal and Lognormal Distribution Coefficients of Variation, Research Paper 609, USDA Forest Products Laboratory, Madison, Wisconsin.
Verrill, S. and Johnson, R.A. (2007) Confidence Bounds and Hypothesis Tests for Normal Distribution Coefficients of Variation, Communications in Statistics Theory and Methods, Volume 36, No. 12, pp 21872206.
See Also
Mean
, SD
, (both supporting weights)
Examples
set.seed(15)
x < runif(100)
CoefVar(x, conf.level=0.95)
# est low.ci upr.ci
# 0.5092566 0.4351644 0.6151409
# Coefficient of variation for a linear model
r.lm < lm(Fertility ~ ., swiss)
CoefVar(r.lm)
# the function is vectorized, so arguments are recyled...
# https://www.itl.nist.gov/div898/software/dataplot/refman1/auxillar/coefvacl.htm
CoefVarCI(K = 0.00246, n = 195, method="vangel",
sides="two.sided", conf.level = c(.5,.8,.9,.95,.99,.999))