## 7 Validation of Simulation Results
These tests were designed to check whether the observed differences (e.g., between sim_1 and sim_2) are significant (\(p\) < 0.05), which allows for the validation of the stability of the simulation and the identification of scenarios that differ significantly in terms of speed, which is crucial for the prediction of road hazards. The results are presented in Table 6, where a positive t-value indicates a higher mean in the first scenario of the pair, and a low \(p\)-value suggests a significant difference. The analysis reveals that only the sim_1 vs. sim_2 pair is substantial for both detectors, confirming the simulation's consistency and highlighting the need for further calibration of parameters, such as speedFactor, in the context of traffic management. The results indicate that for SD_02 and SD_07, the only statistically significant difference (\(p\) < 0.05) occurs between sim_1 and sim_2 (t = 2.026/2.071, \(p\) = 0.044/0.039). A positive t value indicates a higher mean in sim_1, which may reflect more aggressive driver profiles in this scenario. The remaining pairs (e.g., sim_1 vs. sim_3: t = 1.122/1.195, \(p\) = 0.263/0.233; sim_2 vs. sim_3: t = \(-\)1.010/\(-\)0.985, \(p\) = 0.313/0.326) have \(p\) > 0.05, suggesting no significant differences in average speeds, which is consistent with similar simulation configurations (e.g., small changes in speedFactor). Negative t values in some pairs (e.g., sim_2 vs. sim_3) indicate lower averages in sim_2, but these are not statistically significant. Overall, the results confirm the stability of the simulation across scenarios (except for sim_1 vs. sim_2) but highlight the need for multiple replications to draw stronger conclusions. The current \(p\)-values may be overestimated due to the limited sample \begin{table}
\begin{tabular}{c c c c c} \hline \hline
**Pair** & **t-Stat SD\_02** & \(p\)**-Value SD\_02** & **t-Stat SD\_07** & \(p\)**-Value SD\_07** \\ \hline sim\_1 vs. sim\_2 & 2.026 & 0.044 & 2.071 & 0.039 \\ sim\_1 vs. sim\_3 & 1.122 & 0.263 & 1.195 & 0.233 \\ sim\_1 vs. sim\_4 & 1.487 & 0.138 & 1.502 & 0.134 \\ sim\_2 vs. sim\_3 & \(-\)1.010 & 0.313 & \(-\)0.985 & 0.326 \\ sim\_2 vs. sim\_4 & \(-\)0.444 & 0.657 & \(-\)0.467 & 0.641 \\ sim\_3 vs. sim\_4 & 0.504 & 0.615 & 0.453 & 0.651 \\ \hline \hline \end{tabular}
\end{table} 
Table 6: Student’s \(t\)-test results for differences in average speeds between simulation scenarios for detectors SD_02 and SD_07. \begin{table}
\begin{tabular}{c c c c c c c} \hline \hline
**Scenario** & **Mean SD\_02** & **Std Dev SD\_02** & **Conf Int SD\_02** & **Mean SD\_07** & **Std Dev SD\_07** & **Conf Int SD\_07** \\ \hline sim\_1 & 52.47 & 7.91 & 1.27 & 57.23 & 8.22 & 1.26 \\ sim\_2 & 50.34 & 10.28 & 1.65 & 55.08 & 10.51 & 1.62 \\ sim\_3 & 51.42 & 8.35 & 1.34 & 56.12 & 8.63 & 1.33 \\ sim\_4 & 50.97 & 10.63 & 1.70 & 55.63 & 10.94 & 1.68 \\ \hline \hline \end{tabular}
\end{table} 
Table 5: Statistical summary of simulated speed data for SD_02 and SD_07 Detectors. size. For road safety, this implies that sim_1 better models limit violations, which could be the basis for prioritized calibration in future studies. Analysis of vehicle speed data from the SD_02 detector showed varying effectiveness of the four simulations (sim_1, sim_2, sim_3, sim_4) in replicating real traffic. Significantly, priority was given to average speed and drivers' propensity to exceed speed limits. The actual average speed was 52.1 km/h, and sim_1 simulation achieved the closest result (52.5 km/h, a deviation of only 0.4 km/h), demonstrating its high precision in this key metric. The other simulations underperformed the average: sim_2 (50.3 km/h, a deviation of 1.8 km/h), sim_3 (51.4 km/h, a deviation of 0.7 km/h), and sim_4 (50.9 km/h, a deviation of 1.2 km/h). For the percentage of vehicles exceeding 40 km/h (actual: 88.8%), sim_3 came closest (90.1%, overestimation of 1.3%), while sim_1 overestimated (93.4%), and sim_2 and sim_4 underestimated to 80.9% and 81.6%, respectively.