## 4 Numerical Analysis Results and Data Analysis
### Analysis of Variance (ANOVA)  
To find out how significant each factor is compared to the error, an ANOVA table was prepared and the significance of 15 factors (4 main effect factors, 6 interaction factors of 2 factors, 4 interaction factors of 3 factors) was determined. Significance is determined according to the acceptance and rejection of the null hypothesis. An F-test was performed in order to determine whether the null hypothesis should be rejected. The F-value follows the F-distribution, and the F-distribution is according to the ratio of chi squares and shape of F-distribution depends on the degrees of freedom. The F-test is used to test for differences in variance. To determine the significance of factor variance during the F-test, a right-sided test was used in this paper. Equation (2) shows the conditions for rejecting the null hypothesis during the F-test, and Figure 5 shows the conditions for rejecting the null hypothesis from the F distribution during the \begin{table}
\begin{tabular}{c c c c c c c c} \hline \hline  & & \multicolumn{3}{c}{**C1**} & \multicolumn{3}{c}{**C2**} \\ \cline{3-8}  & & **B1** & **B2** & **B3** & **B1** & **B2** & **B3** \\ \hline \multirow{4}{*}{**D1**} & **A1** & 0.00785 & 0.00418 & 0.00495 & 0.00413 & 0.00449 & 0.00412 \\  & **A2** & 0.01267 & 0.00699 & 0.00753 & 0.00554 & 0.00559 & 0.00511 \\  & **A3** & 0.01424 & 0.00805 & 0.01105 & 0.00857 & 0.00949 & 0.00826 \\  & **A4** & 0.01948 & 0.01263 & 0.01393 & 0.01019 & 0.01154 & 0.00999 \\ \hline \multirow{4}{*}{**D2**} & **A1** & 0.01718 & 0.00948 & 0.01213 & 0.00936 & 0.00993 & 0.00918 \\  & **A2** & 0.02542 & 0.01488 & 0.01595 & 0.01206 & 0.01300 & 0.01212 \\  & **A3** & 0.02601 & 0.01318 & 0.01791 & 0.01332 & 0.01559 & 0.01394 \\  & **A4** & 0.03369 & 0.02546 & 0.02866 & 0.02145 & 0.02193 & 0.01585 \\ \hline \hline \end{tabular}  
* A1: no joint, A2: horizontal joint, A3: vertical joint, A4: compound joint; B1: aspect ratio 0.5, B2: aspect ratio 1.0, B3: aspect ratio 1.5, C1: cover depth 2 m, C2: cover depth 4 m; D1: vehicle speed 40 km/h, D2: vehicle speed 80 km/h.  
\end{table} 
Table 7: Four-way table. \begin{table}
\begin{tabular}{c c c c c c c c} \hline \hline  & & \multicolumn{3}{c}{**C1**} & \multicolumn{3}{c}{**C2**} \\ \cline{3-8}  & & **B1** & **B2** & **B3** & **B1** & **B2** & **B3** \\ \hline \multirow{4}{*}{**D  
right-sided test. ANOVA was performed by setting the significance level to 5%. The significance level of 5% value is also the position value of the tail probability (5%) following the F-distribution, and is an index for judging significance. It is the rejection value that determines whether the null hypothesis should be rejected. \[ \begin{array}{l}F_{0}=\frac{V_{x}}{V_{x}}<F(\phi_{x},\phi_{c};\alpha)\text{: Acceptthenullhypothesis(no influence, insignificant)}\\ F_{0}=\frac{V_{x}}{V_{x}}>F(\phi_{x},\phi_{c};\alpha)\text{:Rejectthenullhypothesis( influenced, significant)}\end{array}  \tag{2}\]  
The main effect and the interaction effect were detected through the ANOVA of the data obtained from the experiment. The results of the ANOVA are shown in Table 9. The interaction factors of joint orientation \(\times\) cover depth, aspect ratio \(\times\) vehicle speed, and cover depth \(\times\) vehicle speed showed insignificant results. The interaction factors of joint orientation \(\times\) cover depth, aspect ratio \(\times\) vehicle speed, and cover depth \(\times\) vehicle speed showed insignificant results, so the ANOVA was re-performed by pooling them as error terms. Table 10 shows the results of the ANOVA after pooling non-significant two-factor interaction factors. Figure 5: Right sided test of F-distribution.