# Optimization of Organic Content Removal from Aqueous Solutions by Fenton-Ozonation
## 3 Results
### Fenton Process
#### 3.1.2 ANOVA Analysis of Significant Terms  
Table 5 shows the ANOVA analysis for \(Y_{TOC}\) responses at different treatment durations, after removing the insignificant terms. Each model quality of fitness was improved by removing the terms with high \(p\)-values (>0.1). Keeping only the statistically significant terms that affect the responses, the following models (in coded terms) were determined:  
\[Y_{TOC}^{10 min}=14.4+5.33x_{1}-1.33x_{2}-8.77x_{3}-5.2x_{2}x_{3}-7.81x_{3}^{2} \tag{6}\]  
\[Y_{TOC}^{20 min}=19.4+4.84x_{1}-10.5x_{3}+7.05x_{3}^{2} \tag{7}\]  
\[Y_{TOC}^{30 min}=23.1+7.68x_{1}-15.2x_{3}+13x_{3}^{2} \tag{8}\]  
\[Y_{TOC}^{40 min}=21.6+6.19x_{1}-2.61x_{2}-9.72x_{3}+8.18x_{3}^{2} \tag{9}\]  
\[Y_{TOC}^{60 min}=22.1+6.11x_{1}-3.76x_{2}-11.1x_{3}+2.1x_{1}^{2}+8.08x_{3}^{2} \tag{10}\]  
Table 6 summarizes the main model indicators. \begin{table}
\begin{tabular}{l c c c c c} \hline \hline
**Response** & \(\mathbf{Y_{TOC}^{10 min}}\)**, \%** & \(\mathbf{Y_{TOC}^{20 min}}\)**, \%** & \(\mathbf{Y_{TOC}^{30 min}}\)**, \%** & \(\mathbf{Y_{TOC}^{40 min}}\)**, \%** & \(\mathbf{Y_{TOC}^{60 min}}\)**, \%** \\ \hline R\({}^{2}\) & 0.861 & 0.831 & 0.858 & 0.923 & 0.945 \\ R\({}_{\text{adj}}\)\({}^{2}\) & 0.798 & 0.792 & 0.825 & 0.898 & 0.92 \\ R\({}_{\text{pred}}\)\({}^{2}\) & 0.665 & 0.676 & 0.62 & 0.873 & 0.896 \\ Adequate precision & 14 & 15.4 & 17.8 & 21.4 & 21.8 \\ Lack of fit F-tab & 19.38 & 19.4 & 19.4 & 19.3 & 19.38 \\ Model F-tab & 3.2 & 3.41 & 3.41 & 3.26 & 3.2 \\ \hline \hline \end{tabular}
\end{table} 
Table 6: Statistics of the five obtained models. \begin{table}
\begin{tabular}{c c c c c c c} \hline \hline \multirow{2}{*}{**Source**} & \multicolumn{5}{c}{**Sum of Square; Degrees of Freedom; F-Value; \(p\)-Value \(\times\) 10\({}^{2}\)**} \\ \cline{2-7}  & \(\mathbf{Y_{TOC}^{10 min}}\)**, \%** & \(\mathbf{Y_{TOC}^{20 min}}\)**, \%** & \(\mathbf{Y_{TOC}^{30 min}}\)**, \%** & \(\mathbf{Y_{TOC}^{40 min}}\)**, \%** & \(\mathbf{Y_{TOC}^{60 min}}\)**, \%** \\ \hline Model & 2600; 5; 13.6; 0.02 * & 2610; 3; 21.3; \textless{}0.01 * & 6530; 3; 26.1; \textless{}0.01 * & 2930; 4; 36.1; \textless{}0.01 * & 3340; 5; 37.8; \textless{}0.01 * \\ x\({}_{1}\) & 398; 1; 10.4; 0.81 * & 328; 1; 8.04; 1.14 ** & 826; 1; 9.92; 0.77 * & 536; 1; 26.5; 0.02 * & 522; 1; 29.5; 0.02 * \\ x\({}_{2}\) & 24.9; 1; 0.65; 43.6 & & & 95.5; 1; 4.72; 5.0 *** & 198; 1; 10.8; 0.65 ** \\ x\({}_{3}\) & 1080; 1; 28.2; 0.02 * & 1560; 1; 38.1; \textless{}0.01 * & 3250; 1; 39; \textless{}0.01 * & 1320; 1; 65.3; 0.01 * & 1730; 1; 94.3; \textless{}0.01 * \\ x\({}_{1}\)x\({}_{2}\) & & & & & \\ x\({}_{1}\)x\({}_{3}\) & 216; 1; 5.66; 3.65 *** & & & & \\ x\({}_{2}\) & & & & & & \\ x\({}_{2}\) & & & & & & \\ x\({}_{3}\)\({}^{2}\) & & 885; 1; 23.1; 0.05 * & 721; 1; 17.7; 0.1 * & 2460; 1; 29.5; 0.01 * & 970; 1; 47.9; \textless{}0.01 * & 861; 1; 50.3; \textless{}0.01 * \\ Residual & 421; 11 & 530; 13 & 1080; 13 & 243; 12 & 194; 11 \\ Lack of Fit & 403; 9; 5.12; 17.4 & 428; 11; 0.76; 69.1 & 954; 11; 1.35; 50.2 & 135; 5; 13.5; 25.1 & 114; 9; 0.31; 91 \\ Pure Error & 17.5; 2 & 102; 2 & 129; 2 & 108; 2 & 80.7; 2 \\ \hline \hline \end{tabular}
\end{table} 
Table 5: ANOVA analysis for YTOC responses after different treatment durations, after removing insignificant terms. Based on ANOVA analysis, it was found that all five suggested models can be validated by Fischer tests (model F-value higher than F-tabulated). Also, in terms of F-values, the lack of fit is statistically insignificant (LOF F-value lower than F-tabulated). With the increase of treatment duration, the models describing removal efficiency in terms of TOC are more and more accurate. This is supported by the increase in the values corresponding to the determination coefficient and the adjusted and predicted determination coefficients. Also, the adequate precision indicator is several times higher than the value of four, and increases with treatment duration. Except for the responses at 20 and 30 min of treatment, the three main factors are important in relation to Fenton process performance.