The standard deviation ratio compares the sample standard deviation of predictions with that of observations.
Details
$$\mathrm{SD\ ratio}= \sqrt{\frac{\sum_{i=1}^{n}(pred_i-\bar{pred})^2} {\sum_{i=1}^{n}(obs_i-\bar{obs})^2}}.$$
The ratio is non-negative and one indicates equal variability. Values below
one indicate that predictions have less variability than the observations;
values above one indicate that predictions have more variability than the
observations. It assesses variability, not mean bias or association, and
returns NA with a warning when fewer than two valid pairs remain or the
observations have zero variance. Missing-value handling follows bias().
References
Taylor, K. E. (2001). Summarizing multiple aspects of model performance in a single diagram. Journal of Geophysical Research, 106, 7183-7192. doi:10.1029/2000JD900719
Examples
sd_ratio(1:3, c(1, 3, 2))
#> [1] 1