Coefficient of Variation
Calculates the coefficient of variation and its confidence limits using the noncentral t-distribution..
CoefVar(x, ...) ## S3 method for class 'lm' CoefVar(x, unbiased = FALSE, conf.level = NA, na.rm = FALSE, ...) ## S3 method for class 'aov' CoefVar(x, unbiased = FALSE, conf.level = NA, na.rm = FALSE, ...) ## Default S3 method: CoefVar(x, weights = NULL, unbiased = FALSE, conf.level = NA, na.rm = FALSE, ...)
x |
a (non-empty) 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. |
conf.level |
confidence level of the interval. |
na.rm |
logical. Should missing values be removed? Defaults to FALSE. |
... |
further arguments (not used here). |
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 ≤ft( 1 - \frac{1}{4\cdot(n-1)} + \frac{1}{n} \cdot CV^2 + \frac{1}{2 \cdot (n-1)^2} \right)
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 |
Andri Signorell <andri@signorell.net>,
Michael Smithson <michael.smithson@anu.edu.au> (noncentral-t)
Johnson, B. L., Welch, B. L. (1940). Applications of the non-central t-distribution. Biometrika, 31, 362–389.
Kelley, K. (2007). Sample size planning for the coefcient of variation from the accuracy in parameter estimation approach. Behavior Research Methods, 39 (4), 755-766
Kelley, K. (2007). Constructing confidence intervals for standardized effect sizes: Theory, application, and implementation. Journal of Statistical Software, 20 (8), 1-24
McKay, A. T. (1932). Distribution of the coefficient of variation and the extended t distribution, Journal of the Royal Statistical Society, 95, 695–698.
Smithson, M.J. (2003) Confidence Intervals, Quantitative Applications in the Social Sciences Series, No. 140. Thousand Oaks, CA: Sage. pp. 39-41
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)
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