S/N

Statistical Measures

FORMULA

References

1.

Root Mean Squared

Error

$RMSE={\left[{\displaystyle \sum _{i=1}^N\frac{1}{N}{\left(M{R}_{exp,i}-M{R}_{pre,i}\right)}^2}\right]}^{\frac{1}{2}}$

[19]

2.

Mean Bias Error

$MBE=\frac{1}{N}{\displaystyle \sum _{i=1}^N\left(M{R}_{pre,i}-M{R}_{exp,i}\right)}$

[107]

3.

Chi Squared or Reduced Chi Squared

$x^2={{\displaystyle \sum _{i=1}^n\frac{\left(M{R}_{exp,i}-M{R}_{pre,i}\right)}{N-n}}}^2$

[19]

4.

Mean Relative Deviation Modulus

$P\left(\%\right)=\frac{100}{N}{\displaystyle \sum _{i=1}^N\left|\frac{M{R}_{Qi}-M{R}_{ei}}{M{R}_{ei}}\right|}$

[108]

5.

Coefficient of Determination

$R^2=1-\frac{{\displaystyle \sum _{i=1}^n{\left(M{R}_{exp,i}{}_i-M{R}_{pre,i}\right)}^2}}{{\displaystyle \sum _{i=1}^n{\left(M{R}_{exp,i}-M{R}_{pre,i}\right)}^2}}$

[29]

6.

Sum Square Error

$SSE=\frac{1}{N}{\displaystyle \sum _{i=1}^N{\left(M{R}_{exp,i}-M{R}_{pre,i}\right)}^2}$

[109]

7.

Modelling Efficiency

$EF=\frac{{\displaystyle \sum _{i=1}^N{\left(M{R}_{i,\exp }-M{R}_{i,ex{p}_{mean}}\right)}^2-{\displaystyle \sum _{i=1}^N{\left(M{R}_{i,pre}-M{R}_{i,exp}\right)}^2}}}{{\displaystyle \sum _{i=1}^N{\left(M{R}_{i,exp}-M{R}_{i,ex{p}_{mean}}\right)}^2}}$

[90]

8.

Correlation coefficient

$r=\frac{N{\displaystyle \sum _{i=1}^{N}M{R}_{pre,i}M{R}_{exp,i}}-{\displaystyle \sum _{i=1}^{N}M{R}_{pre,i}{\displaystyle \sum _{i=1}^{N}M{R}_{exp,i}}}}{\sqrt{\left(N{\displaystyle \sum _{i=1}^{N}M{R}_{pre,i}^2-{\left({\displaystyle \sum _{i=1}^{N}M{R}_{pre,i}}\right)}^2}\right)\left(N{\displaystyle \sum _{i=1}^{N}M{R}_{exp,i}^2-{\left({\displaystyle \sum _{i=1}^{N}M{R}_{exp,i}}\right)}^2}\right)}}$

[16]

9.

Mean Relative Deviation

$E\left(\%\right)=\frac{100}{N}{\displaystyle \sum _{i=1}^N\left|\frac{\text{Experimentalvalue}-\text{Predictedvalue}}{\text{Experimentalvalue}}\right|}$

[43]

10.

Residual Sum of Squares

$RSS={\displaystyle \sum _{i=1}^N{\left(M{R}_{exp,i}-M{R}_{pred,i}\right)}^2}$

[85]