## 4 Results
### Variance Analysis  
Analysis of variance is a quantitative technique that can determine the degrees of influence and confidence of each factor on the performance results [29,31]. By comparing the average sum of the square of the deviations between factors and errors, \(F\) values are obtained, which reflect the extent of the influence of changes in levels of factors on the test indices [32,33]. Based on the given significance level \(\alpha\) (confidence), the critical value \(F_{\alpha}\) (\(f_{\text{f}}\),\(f_{\text{e}}\)) is sought from the \(F\)-distribution table according to the degrees of freedom. The determination of the significance of influences is demonstrated in Table 4[34]. The \(F\) value is given by:  
\[F=\frac{S_{\text{f}}/f_{\text{f}}}{S_{\text{e}}/f_{\text{e}}} \tag{16}\]  
where, \(S_{\text{f}}\) and \(f_{\text{f}}\) represent the sum of the squares of the deviations and the number of degrees of freedom of each factor, respectively; and \(S_{\text{e}}\) and \(f_{\text{e}}\) represent the sum of the squares of the deviations and number of degree of freedom of errors in the test, respectively. The analysis of variance was conducted on the orthogonal test results with SPSS statistical analysis software (Table 5). \begin{table}
\begin{tabular}{c c c c} \hline
**Serial Number** & **Range of \(F\)** & **Sensitivity Statement** & **Degree** \\ \hline
1 & \(F>F_{0.001}(f_{\text{f}}\),\(f_{\text{e}}\)) & Highly significant effects & *** \\
2 & \(F_{0.001}(f_{\text{f}}\),\(f_{\text{e}}\)) \(>F>F_{0.01}(f_{\text{f}}\),\(f_{\text{e}}\)) & Significant effects & ** \\
3 & \(F_{0.01}(f_{\text{f}}\),\(f_{\text{e}}\)) \(>F>F_{0.05}(f_{\text{f}}\),\(f_{\text{e}}\)) & General effects & * \\
4 & \(F<F_{0.05}(f_{\text{f}}\),\(f_{\text{e}}\)) & Insignificant effects & \\ \hline \end{tabular} Notes: \(F_{0.001}(f_{\text{f}}\),\(f_{\text{e}})\) = 141.1, \(F_{0.01}(f_{\text{f}}\),\(f_{\text{e}})\) = 29.46, and \(F_{0.05}(f_{\text{f}}\),\(f_{\text{e}})\) = 9.28.  
\end{table} 
Table 4: Determination of level of significance. Figure 8: The change curves of the horizontal displacement and the volume of the plastic zone for various factors. (**a**) Cutting height. (**b**) Breaking position of main roof. (**c**) Support strength. (**d**) Sidewall-protecting force. \begin{table}
\begin{tabular}{c c c c c c} \hline
**Index** & **Source Variance** & **Sum of the Squared Deviation** & **Degrees of Freedom** & \(F\) & **Significance** \\ \hline \multirow{4}{*}{\
\begin{tabular}{c} Horizontal \\ displacement \\ \end{tabular} } & Cutting height & 82,486.15 & 3 & 20.17 & * \\  & Breaking position of main roof & 134,689.21 & 3 & 32.94 & ** \\  & Support strength & 1147.76 & 3 & 0.28 & \\  & Sidewall-protecting force & 3687.77 & 3 & 0.90 & \\ \hline \multirow{4}{*}{
\begin{tabular}{c} Volume of \\ plastic zone \\ \end{tabular} } & Cutting height & 265.15 & 3 & 400.07 & *** \\  & Breaking position of main roof & 103.96 & 3 & 156.85 & *** \\ \cline{1-1}  & Support strength & 7.87 & 3 & 11.88 & * \\ \cline{1-1}  & Sidewall-protecting force & 0.87 & 3 & 1.30 & \\ \hline \end{tabular}
\end{table} 
Table 5: Results of analysis of variance. As shown in Table 5:  
1. In terms of the horizontal displacement, the breaking position of the main roof has significant effects, while the cutting height exerts a more moderate, general influence (the other factors exert insignificant effects). According to the sensitivity, the breaking position of the main roof, cutting height, sidewall-protecting force, and support strength are ranked thus (in descending order). 2. For the volume of the plastic zone, the cutting height and the breaking position of the main roof have highly significant influences, and the significance of the former is greater than that of the latter. Furthermore, the support strength has general effects, while the other factors exert insignificant influences. In accordance with their sensitivity, the cutting height, breaking position of the main roof, support strength, and sidewall-protecting force are ranked in descending order. 3.