Compute the coefficient of variation (CV, ratio of the standard deviation to the mean, \(\sigma/\mu\)) for a set of numeric values.
coef_var(x, ...)distribution_coef_var(x, ...)
# S3 method for numeric
coef_var(
x,
mu = NULL,
sigma = NULL,
method = c("standard", "unbiased", "median_mad", "qcd"),
trim = 0,
remove_na = FALSE,
n = NULL,
...
)
The computed coefficient of variation for 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.
A numeric vector of mean values to use to compute the coefficient
of variation. If supplied, x is not used to compute the mean.
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 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]: \((Q_3 - Q_1)/(Q_3 + Q_1)\).
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.
Logical. Should NA values be removed before computing (TRUE)
or not (FALSE, default)?
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?
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] 1.239094coef_var(sandwiches / 2) # same
#> [1] 1.239094
coef_var(sandwiches + 4) # different! 0 is no longer meaningful!
#> [1] 0.6290784
coef_var(1:10)
coef_var(c(1:10, 100), method = "median_mad")
coef_var(c(1:10, 100), method = "qcd")
coef_var(mu = 10, sigma = 20)
coef_var(mu = 10, sigma = 20, method = "unbiased", n = 30)
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