Skip to contents

Adjusted Coefficient of Variation

Source: R/acv.R
acv.Rd

[Stable]

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.

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

Author

Tiago Olivoto tiagoolivoto@gmail.com

Examples

# \donttest{
################# 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)
#> # A tibble: 15 × 7
#>     mean    var log10_mean log10_var    POLAR    cv   acv
#>    <dbl>  <dbl>      <dbl>     <dbl>    <dbl> <dbl> <dbl>
#>  1 0.589 0.0064    -0.230     -2.19  -0.326   13.6   7.34
#>  2 0.617 0.0141    -0.210     -1.85  -0.00356 19.2  10.6 
#>  3 0.794 0.0218    -0.100     -1.66   0.0703  18.6  11.6 
#>  4 1.03  0.0318     0.0133    -1.50   0.115   17.3  12.2 
#>  5 1.50  0.0314     0.177     -1.50  -0.0624  11.8   9.94
#>  6 3.86  0.0766     0.587     -1.12  -0.106    7.17  9.46
#>  7 4.70  0.062      0.672     -1.21  -0.287    5.30  7.68
#>  8 6.11  0.0822     0.786     -1.09  -0.285    4.69  7.70
#>  9 7.15  0.160      0.854     -0.795 -0.0658   5.60  9.91
#> 10 7.53  0.199      0.877     -0.702  0.00298  5.91 10.7 
#> 11 1.22  0.0157     0.0874    -1.80  -0.269   10.2   7.84
#> 12 1.63  0.0593     0.213     -1.23   0.176   14.9  13.1 
#> 13 2.43  0.0565     0.385     -1.25  -0.0263   9.78 10.4 
#> 14 2.50  0.200      0.398     -0.700  0.509   17.9  19.2 
#> 15 3.02  0.272      0.479     -0.566  0.557   17.3  20.3 
# }