Compute the coefficient of variation

Compute the coefficient of variation (CV, ratio of the standard deviation to the mean, \(\sigma/\mu\)) for a set of numeric values.

Usage

coef_var(x, ...)

distribution_coef_var(x, ...)

# S3 method for class 'numeric'
coef_var(
  x,
  mu = NULL,
  sigma = NULL,
  method = c("standard", "unbiased", "median_mad", "qcd"),
  trim = 0,
  remove_na = FALSE,
  n = NULL,
  ...
)

Arguments

x

A numeric vector of ratio scale (see details), or vector of values than can be coerced to one.

...

Further arguments passed to computation functions.

mu

A numeric vector of mean values to use to compute the coefficient of variation. If supplied, x is not used to compute the mean.

sigma

A numeric vector of standard deviation values to use to compute the coefficient of variation. If supplied, x is not used to compute the SD.

method

Method to use to compute the CV. Can be "standard" to compute by dividing the standard deviation by the mean, "unbiased" for the unbiased estimator for normally distributed data, or one of two robust alternatives: "median_mad" to divide the median by the stats::mad(), or "qcd" (quartile coefficient of dispersion, interquartile range divided by the sum of the quartiles [twice the midhinge]: \((Q_3 - Q_1)/(Q_3 + Q_1)\).

trim

the fraction (0 to 0.5) of values to be trimmed from each end of x before the mean and standard deviation (or other measures) are computed. Values of trim outside the range of (0 to 0.5) are taken as the nearest endpoint.

remove_na

Logical. Should NA values be removed before computing (TRUE) or not (FALSE, default)?

n

If method = "unbiased" and both mu and sigma are provided (not computed from x), what sample size to use to adjust the computed CV for small-sample bias?

Value

The computed coefficient of variation for x.

Details

CV is only applicable of values taken on a ratio scale: values that have a fixed meaningfully defined 0 (which is either the lowest or highest possible value), and that ratios between them are interpretable For example, how many sandwiches have I eaten this week? 0 means "none" and 20 sandwiches is 4 times more than 5 sandwiches. If I were to center the number of sandwiches, it will no longer be on a ratio scale (0 is no "none" it is the mean, and the ratio between 4 and -2 is not meaningful). Scaling a ratio scale still results in a ratio scale. So I can re define "how many half sandwiches did I eat this week ( = sandwiches * 0.5) and 0 would still mean "none", and 20 half-sandwiches is still 4 times more than 5 half-sandwiches.

This means that CV is NOT invariant to shifting, but it is to scaling:

sandwiches <- c(0, 4, 15, 0, 0, 5, 2, 7)
coef_var(sandwiches)
#> [1] 1.239094

coef_var(sandwiches / 2) # same
#> [1] 1.239094

coef_var(sandwiches + 4) # different! 0 is no longer meaningful!
#> [1] 0.6290784

Examples

coef_var(1:10)
#> [1] 0.5504819
coef_var(c(1:10, 100), method = "median_mad")
#> [1] 0.7413
coef_var(c(1:10, 100), method = "qcd")
#> [1] 0.4166667
coef_var(mu = 10, sigma = 20)
#> [1] 2
coef_var(mu = 10, sigma = 20, method = "unbiased", n = 30)
#> [1] 2.250614