## 3 Results
### Analysis of Variance
#### 3.2.2 Four Locking Screws  
The maximum principal stress of four locking screws results from running the FEA model at various testing conditions, as shown in Table 9. All main factors were identified in importance by an ANOVA, as shown in Table 10. Furthermore, R-squared and adjusted R-squared statistics were analyzed for checking the fit of the dataset. Moreover, if the p-value of each main effect and its interaction was less than 0.05, it was considered statistically significant. According to this analysis, gap type (A), fracture gap (B), fixation techniques (D), the interaction between the variables A and D, and the interaction between the variables A and B were factors that affected the maximum principal stress of the composite interlocking nail in the same way as two screws.  
The R\({}^{2}\) value shows that the model explains 75.04% of the variance in the maximum principal stress, which indicates that the model fits the data well.  
The residual plot of the maximum principal stress is shown in Figure 9, representing the normal probability plot of the residuals. The residuals of the response randomly scatter around zero in the residual plots. Regarding the residuals versus the fits, the observation points (blue dots) scattered randomly in the normal probability plot show that the process parameters in this study were normal and independently distributed. The histogram of the residuals is approximately symmetric. Regarding the residuals versus the order, the residuals exhibit no clear pattern.  
Figure 8: Pareto chart of the effects of principal stress (two locking screws).  
\begin{table}
\begin{tabular}{c c c c c c c c c c c c c c c c c c} \hline \hline \multirow{2}{*}{**Condition**} & **A** & **B** & **C** & **D** & \multicolumn{3}{c}{**Principal**} & **Condition** & **A** & **B** & **C** & **D** & \multicolumn{3}{c}{**Principal**} & **Condition** & **A** & **B** & **C** & **D** & \multicolumn{3}{c}{**Principal**} \\  & & & & & & & & &  
The magnitude and significance of an effect were determined by the Pareto chart shown in Figure 10. The Pareto chart shows the absolute values from the largest to the smallest effect of the standardized effects. The standardized effects are t-statistics that test the null hypothesis that the effect is zero [31]. In this Pareto chart, the bars that represent factors A, AD, D, B, and AB cross the reference line, which is at 1.989. These factors are statistically significant at the 0.05 level with the current model terms. In the selected range, the infection order of each factor is A \(>\) AD \(>\) D \(>\) B \(>\) AB. This means that the variable A and the interaction between variables A and D are potentially the most and second-most important, respectively. The third-most important is the variable D. The variable B and the interaction between variables A and B are considered the fourth- and the fifth-most important effects regarding the maximum principal stress by the statistical model analysis.  
\begin{table}
\begin{tabular}{l c c c c c} \hline \hline
**Source** & **DF** & **Adj. SS** & **Adj. MS** & **F-Value** & **P-Value** \\ \hline Model & 17 & 200,355 & 11,785.6 & 14.50 & 0.000 \\ Linear & 7 & 110,188 & 15,741.2 & 19.37 & 0.000 \\ A & 2 & 83,008 & 41,504.1 & 51.07 & 0.000 \\ B & 2 & 7771 & 3885.4 & 4.78 & 0.011 \\ D & 3 & 19,172 & 6390.7 & 7.86 & 0.000 \\
2-Way Interactions & 10 & 48,725 & 4872.5 & 6.00 & 0.000 \\ A*B & 4 & 8580 & 2145.1 & 2.64 & 0.040 \\ A*D & 6 & 40,557 & 6759.4 & 8.32 & 0.000 \\ \hline Error & 82 & 66,637 & 812.7 & & \\ \hline Total & 99 & 266,993 & & & \\ \hline \hline \end{tabular}  
\end{table}
Table 10: Analysis of variance for principal stress (four locking screws).  
Figure 9: The residual plot of principal stress (four locking screws).