# Integrating Root Morphology Based on Whole-Pullout Test of Model Roots: A Case Study
## 3 Results
### Analysis of Variance  
The range analysis results do not reveal the significance of the influencing factors. However, a variance analysis can assess the significance of each influencing factor on the pullout resistance of roots. The calculated results of the pullout resistance experiments are presented, showing the deviation sum of squares, degrees of freedom, mean squares, and \(F\)-values for each factor in Table 5. It is observed that the mean square for factor D is 162.48, which is less than the mean square of the error column (442.64), indicating that the branching angle of the lateral root has a relatively small impact on the experimental results and is considered a secondary factor. It is therefore categorized as part of the error term, and the sum of squares, degrees of freedom, and mean square for the error are recalculated. Setting the significance level at \(\alpha=0.01\), the critical value \(F_{0.01}(3,6)=9.78\) is obtained from the table. Since \(F_{B}=17.36\) is greater than \(F_{0.01}(3,6)=9.78\), it can be concluded that the influence of the number of lateral roots on the results is highly significant. Setting the significance level at \(\alpha=0.05\), the critical value \(F_{0.05}(3,6)=4.76\) is obtained, and since \(F_{0.05}(3,6)=4.76\) is less than \(F_{C}=6.38\) but greater than \(F_{0.01}(3,6)=9.78\), it can be concluded that the influence of the main root length on the results is significant. Setting the significance level at \(\alpha=0.1\), the critical value \(F_{0.1}(3,6)=3.29\) is obtained, and since \begin{table}
\begin{tabular}{c c c c c c} \hline \hline \multirow{2}{*}{**Factors**} & \multicolumn{2}{c}{**A**} & **B** & **C** & **D** & **Error** \\  & \multicolumn{2}{c}{**(Compaction**} & **(Number of Lateral** & **(Taroot** & **(Branching Angle of the Lateral Roots/deg)** & **Column** \\  & **Frequency/freq)** & **Roots/pcs)** & **Length/cm)** & **(Branching Angle of the Lateral Roots/deg)** & **Column** \\ \hline \multirow{4}{*}{\(K_{i}\)} & \(K_{1}\) & 254.2 & 200.0 & 252.5 & 305.8 & 274.9 \\  & \(K_{2}\) & 317.4 & 240.0 & 271.6 & 348.4 & 367.5 \\  & \(K_{3}\) & 371.7 & 393.3 & 396.7 & 329.1 & 355.8 \\  & \(K_{4}\) & 405.0 & 515.0 & 427.5 & 365.0 & 350.1 \\  & \(k_{1}\) & 63.6 & 50.0 & 63.1 & 76.5 & 68.7 \\  & \(k_{2}\) & 79.4 & 60.0 & 67.9 & 87.1 & 91.9 \\  & \(k_{3}\) & 92.9 & 98.3 & 99.2 & 82.3 & 89.0 \\  & \(k_{4}\) & 101.3 & 128.8 & 106.9 & 91.3 & 87.5 \\ \(R_{j}=\max\{K_{i}\}-\min\{K_{i}\}\) & 150.8 & 315.0 & 175.0 & 59.2 & 92.6 \\ \multicolumn{2}{c}{Factor Priority} & \multicolumn{2}{c}{B \(\rightarrow\) C \(\rightarrow\) A \(\rightarrow\) D} \\ \multicolumn{2}{c}{Optimal Solution} & \multicolumn{2}{c}{B\({}_{4}\)C\({}_{4}\)A\({}_{4}\)D\({}_{4}\)} \\ \hline \hline \end{tabular}
\end{table} 
Table 4: Summary of the range analysis. \begin{table}
\begin{tabular}{c c c c c c c} \hline \hline \multirow{2}{*}{**Group Number**} & \multirow{2}{*}{**Measured Value/N**} & \multirow{2}{*}{**Mean Value/N**} & **30\% of the Mean** & **Range/N** & **Pullout Resistance** \\  & & & & **Value/N** & **Characteristic Value/N** \\ \hline
1 & 60 & 60 & 65 & 61.7 & 18.5 & 5 & 61.7 \\
2 & 120 & 120 & 140 & 126.7 & 38 & 20 & 126.7 \\
3 & 140 & 140 & 140 & 140 & 42 & 0 & 140 \\
4 & 40 & 35 & 40 & 38.3 & 11.5 & 5 & 38.3 \\
5 & 65 & 65 & 70  
\(F_{0.1}(3,6)=3.29\) is less than \(F_{A}=3.60\) but greater than \(F_{0.05}(3,6)=4.76\), it can be concluded that the unit weight of soil around the root has a certain impact on the results. In summary, consistent with the range analysis results, the significance levels of the influencing factors in the experiment are in the following order: number of lateral roots > taproot length > unit weight of soil around the root > branching angle of the lateral root.