Name  Error equation  Note  Ref. 
SSE/ERRSQ  $\sum}_{i=1}^{n}{\left({q}_{e,cal}{q}_{e,exp}\right)}^{2$  It is indicator for accuracy, in which the best fit of the data can be assessed from the sumofsquares value. The smallest value for SSE indicates the best fit data for the model.  [82] 
HYBRID  $\sum}_{i=1}^{n}\frac{100}{np}\left[\frac{\left({q}_{e,meas}{q}_{e,cal}\right)}{{q}_{e,meas}}\right]$  The error function was developed to improve ERRSQ fit at low concentrations.  [83] 
ARE  $\frac{100}{n}{\displaystyle \sum}_{i=1}^{n}\left\frac{\left({q}_{e,meas}{q}_{e,cal}\right)}{{q}_{e,meas}}\right$  which indicates a tendency to under or overestimate the experimental data, attempts to minimize the fractional error distribution across the entire studied concentration range  [84] 
χ^{2}  $\sum}_{i=1}^{n}\frac{{\left({q}_{e,cal}{q}_{e,\mathrm{exp}}\right)}^{2}}{{q}_{e,cal}$  χ^{2} is also similar to SSE. Smaller values of χ^{2} also indicate a better fit of the model.  [69] 
SE  $\sqrt{\frac{1}{n}{\displaystyle \sum}_{i=1}^{n}{\left({q}_{e,cal}{q}_{e,exp}\right)}^{2}}$  It is also used to judge the equilibrium model. A smaller value for SE indicates a better fit of the model  [84] 
∆q (%)  $100\sqrt{\frac{1}{n1}{\displaystyle \sum}_{i=1}^{n}{\left(\frac{{q}_{e,meas}{q}_{e,cal}}{{q}_{e,meas}}\right)}^{2}}$  According to the number of degrees of freedom in the system, it is similar to some respects of a modified geometric mean error distribution 

R^{2}  $\frac{{{\displaystyle \sum}}_{i=1}^{n}{\left({q}_{cal}\overline{{q}_{exp}}\right)}^{2}}{{{\displaystyle \sum}}_{i=1}^{n}{\left({q}_{e,cal}\overline{{q}_{e,exp}}\right)}^{2}+{{\displaystyle \sum}}_{i=1}^{n}{\left({q}_{e,cal}{q}_{e,exp}\right)}^{2}}$  The correlation coefficient (R^{2}) is the common measure of analytical accuracy. Its value is within the range of 0 < R^{2} ≤ 1, where a high value reflects an accurate analysis.  [85] 
SAE  $\sum}_{i=1}^{n}\left{q}_{e,mass}{q}_{e,cal}\right$  with an increase in the errors will provide a better fit, leading to the bias towards the high concentration data  [84] 
S_{RE}  $\sqrt{\frac{\left[{{\displaystyle \sum}}_{i=1}^{n}{\left({q}_{e,mass}{q}_{e,cal})\text{ARE}\right)}^{2}\right]}{n1}}$ 
 [84] 