R: Coefficient of Variation

CoefVar {DescTools} | R Documentation

## Coefficient of Variation

### Description

Calculates the coefficient of variation and its confidence limits using the noncentral `t`-distribution..

### Usage

    CoefVar(x, unbiased = FALSE, conf.level = NA, na.rm = FALSE, ...)

    ## 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, unbiased = FALSE, conf.level = NA, na.rm = FALSE, ...)

### Arguments

`x` | a (non-empty) numeric vector of data values.
`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).

### 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 ≤ft( 1 - \frac{1}{4\cdot(n-1)} + \frac{1}{n} \cdot CV^2 + \frac{1}{2 \cdot (n-1)^2} \right)

### 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> (noncentral-t)

### References

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

### See Also

`mean`, `sd`

### 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)

[Package DescTools version 0.99.26 Index]