Name

Error equation

Note

Ref.

SSE/ERRSQ

i = 1 n ( q e , c a l q e , e x p ) 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.

[82]

HYBRID

i = 1 n 100 n p [ ( q e , m e a s q e , c a l ) q e , m e a s ]

The error function was developed to improve ERRSQ fit at low concentrations.

[83]

ARE

100 n i = 1 n | ( q e , m e a s q e , c a l ) q e , m e a s |

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]

χ2

i = 1 n ( q e , c a l q e , exp ) 2 q e , c a l

χ2 is also similar to SSE. Smaller values of χ2 also indicate a better fit of the model.

[69]

SE

1 n i = 1 n ( q e , c a l q e , e x p ) 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 1 n 1 i = 1 n ( q e , m e a s q e , c a l q e , m e a s ) 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

i = 1 n ( q c a l q e x p ¯ ) 2 i = 1 n ( q e , c a l q e , e x p ¯ ) 2 + i = 1 n ( q e , c a l q e , e x p ) 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.

[85]

SAE

i = 1 n | q e , m a s s q e , c a l |

with an increase in the errors will provide a better fit, leading to the bias towards the high concentration data

[84]

SRE

[ i = 1 n ( q e , m a s s q e , c a l ) ARE ) 2 ] n 1

[84]