acv {metan}

Adjusted Coefficient of Variation

Description

Computes the scale-adjusted coefficient of variation, acv, (Doring and Reckling, 2018) to account for the systematic dependence of \(\sigma^2\) from \(\mu\). The acv is computed as follows: \[acv = \frac{\sqrt{10^{\tilde v_i}}}{\mu_i}\times 100\] where \(\tilde v_i\) is the adjusted logarithm of the variance computed as: \[\tilde v_i = a + (b - 2)\frac{1}{n}\sum m_i + 2m_i + e_i\] being \(a\) and \(b\) the coefficients of the linear regression for \(log_{10}\) of the variance over the \(log_{10}\) of the mean; \( m_i\) is the \(log_{10}\) of the mean, and \( e_i\) is the Power Law Residuals (POLAR), i.e., the residuals for the previously described regression.

Usage

acv(mean, var, na.rm = FALSE)

Arguments

mean

A numeric vector with mean values.

var

A numeric vector with variance values.

na.rm

If FALSE, the default, missing values are removed with a warning. If TRUE, missing values are silently removed.

Value

A tibble with the following columns

• mean The mean values;

• var The variance values;

• log10_mean The base 10 logarithm of mean;

• log10_var The base 10 logarithm of variance;

• POLAR The Power Law Residuals;

• cv The standard coefficient of variation;

• acv Adjusted coefficient of variation.

Author(s)

Tiago Olivoto [e-mail]

References

Doring, T.F., and M. Reckling. 2018. Detecting global trends of cereal yield stability by adjusting the coefficient of variation. Eur. J. Agron. 99: 30-36. doi:10.1016/j.eja.2018.06.007

Examples

################# Table 1 from Doring and Reckling (2018)  ###########

# Mean values
u <- c(0.5891, 0.6169, 0.7944, 1.0310, 1.5032, 3.8610, 4.6969, 6.1148,
       7.1526, 7.5348, 1.2229, 1.6321, 2.4293, 2.5011, 3.0161)

# Variances
v <- c(0.0064, 0.0141, 0.0218, 0.0318, 0.0314, 0.0766, 0.0620, 0.0822,
       0.1605, 0.1986, 0.0157, 0.0593, 0.0565, 0.1997, 0.2715)

library(metan)
acv(u, v)