TABLE 3.

Some measures of agreement between observations and predictions that can be used to assess TBI models.

Level of agreement test	Formula	Range	Agreement rating
Index of agreement dr	$d_r=\left[\begin{array}{ccc}1-\frac{\sum \left|O_i-P_i\right|}{2\sum \left|O_i-\overline{O}\right|}& \text{if}& \sum \left|O_i-P_i\right|\le 2\sum \left|O_i-\overline{O}\right|\\ \frac{\sum \left|O_i-P_i\right|}{2\sum \left|O_i-\overline{O}\right|}-1& \text{if}& \sum \left|O_i-P_i\right|>2\sum \left|O_i-\overline{O}\right|\end{array}\right]$	− 1 to 1	↑ dr ≡ better agreement
Coefficient of efficiency (E2)	$E_2=1-\frac{\sum {\left|O_i-P_i\right|}^2}{\sum {\left|O_i-\overline{O}\right|}^2}$	− ∞ to 1	↑ E2 ≡ better agreement
RMSE to observations
Standard deviation ratio (RSR)	$\text{RSR}=\frac{\sqrt{{\left(O_i-P_i\right)}^2}}{\sqrt{\sum {\left(O_i-\overline{O}\right)}^2}}$	0 to ∞	↓ RSR ≡ better agreement
Correlation score (CS)	$CS=(1-|NISE|)\times 100$ $\mathit{\text{NISE}}=1-\frac{2\sum O_i{P}_i}{\sum O_i^2+\sum P_i^2}$	0–100	86–100 excellent 65–86 good 44–65 fair 26–44 marginal 0–26 unacceptable