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 sum-of-squares value. The smallest value for SSE indicates the best fit data for the model.  HYBRID $\sum _{i=1}^{n}\frac{100}{n-p}\left[\frac{\left({q}_{e,meas}-{q}_{e,cal}\right)}{{q}_{e,meas}}\right]$ The error function was developed to improve ERRSQ fit at low concentrations.  ARE $\frac{100}{n}\sum _{i=1}^{n}|\frac{\left({q}_{e,meas}-{q}_{e,cal}\right)}{{q}_{e,meas}}|$ which indicates a tendency to under or overestimate the experimental data, attempts to minimize the fractional error distribution across the entire studied concentration range  χ2 $\sum _{i=1}^{n}\frac{{\left({q}_{e,cal}-{q}_{e,\mathrm{exp}}\right)}^{2}}{{q}_{e,cal}}$ χ2 is also similar to SSE. Smaller values of χ2 also indicate a better fit of the model.  SE $\sqrt{\frac{1}{n}\sum _{i=1}^{n}{\left({q}_{e,cal}-{q}_{e,exp}\right)}^{2}}$ It is also used to judge the equilibrium model. A smaller value for SE indicates a better fit of the model  ∆q (%) $100\sqrt{\frac{1}{n-1}\sum _{i=1}^{n}{\left(\frac{{q}_{e,meas}-{q}_{e,cal}}{{q}_{e,meas}}\right)}^{2}}$ According to the number of degrees of freedom in the system, it is similar to some respects of a modified geometric mean error distribution R2 $\frac{{\sum }_{i=1}^{n}{\left({q}_{cal}-\overline{{q}_{exp}}\right)}^{2}}{{\sum }_{i=1}^{n}{\left({q}_{e,cal}-\overline{{q}_{e,exp}}\right)}^{2}+{\sum }_{i=1}^{n}{\left({q}_{e,cal}-{q}_{e,exp}\right)}^{2}}$ The correlation coefficient (R2) is the common measure of analytical accuracy. Its value is within the range of 0 < R2 ≤ 1, where a high value reflects an accurate analysis.  SAE $\sum _{i=1}^{n}|{q}_{e,mass}-{q}_{e,cal}|$ with an increase in the errors will provide a better fit, leading to the bias towards the high concentration data  SRE $\sqrt{\frac{\left[{\sum }_{i=1}^{n}{\left({q}_{e,mass}-{q}_{e,cal}\right)-\text{ARE}\right)}^{2}\right]}{n-1}}$