## 7 Validation of Simulation Results
The simulation data selected for presentation are the result of single runs in SUMO for a given set of configuration parameters. This fact makes it impossible to calculate standard deviations or confidence intervals directly between replications. However, these are very important and basic measures necessary for data evaluation. For this reason, the data used to present the results were used to estimate statistical measures. These are presented in Table 5. However, these values are approximations of the variability in single runs and do not replace the need for hypothesis testing. Such tests will be carried out in future studies with multiple replications. They will use selected simulation configuration sets, selected during this study. \begin{table}
\begin{tabular}{c c c c c c c c c c} \hline \hline \multirow{2}{*}{**Scenario**} & **Speed Real** & **Average** & **\%\textgreater{}40 km/h** & **\%\textgreater{}40 km/h** & **\%\textgreater{}50 km/h** & **\%\textgreater{}50 km/h** & **Compliance** & **RMSE** & \multirow{2}{*}{**CSAS**} \\  & [km/h] & **Sim. [km/h]** & **Real [km/h]** & **Sim. [\%]** & **Real [\%]** & **Sim. [\%]** & **[\%]** & **[km/h]** & **CSAS** \\ \hline \hline
**sim\_1** & 56.6 & 57.2 & 95.2 & 98.8 & 80.6 & 78.2 & 93.9 & 12.20 & 80.8 \\
**sim\_2** & 56.6 & 55.1 & 95.2 & 91.5 & 80.6 & 67.9 & 94.6 & 13.80 & 78.9 \\
**sim\_3** & 56.6 & 56.1 & 95.2 & 96.4 & 80.6 & 72.7 & 94.4 & 12.50 & 79.7 \\
**sim\_4** & 56.6 & 55.6 & 95.2 & 91.5 & 80.6 & 69.1 & 94.5 & 14.10 & 79.4 \\ \hline \hline \end{tabular}
\end{table} 
Table 4: Summary results of four simulation scenarios for the SD_07 detector. Figure 14: Comparison of velocity distributions of all simulation scenarios with real data for the SD_07 detector (source: own development). \begin{table}
\begin{tabular}{c c c c c c c c c c} \hline \hline \multirow{2}{*}{**Scenario**} & **Speed Real** & **Average** & **\%\textgreater{}40 km/h** & **\%\textgreater{}40 km/h** & **\%\textgreater{}50 km/h** & **\%\textgreater{}50 km/h** & **Compliance** & **RMSE** & \multirow{2}{*}{**CSAS**} \\  & [km/h] & **Sim. [km/h]** & **Real [km/h]** & **Sim. [\%]** & **Real [\%]** & **Sim. [\%]** & **[\%]** & **[km/h]** & **CSAS** \\ \hline \hline
**sim\_1** & 52.1 & 52.5 & 88.8 & 93.4 & 61.2 & 61.2 & 89.3 & 11.80 & 80.2 \\
**sim\_2** & 52.1 & 50.3 & 88.8 & 80.9 & 61.2 & 48.0 & 92.0 & 13.70 & 75.8 \\
**sim\_3** & 52.1 & 51.4 & 88.8 & 90.1 & 61.2 & 57.2 & 90.6 & 12.10 & 79.8 \\
**sim\_4** & 52.1 & 50.9 & 88.8 & 81.6 & 61.2 & 52.6 & 93.6 & 13.90 & 77.6 \\ \hline \hline \end{tabular}
\end{table} 
Table 3: Summary results of four simulation scenarios for the SD_02 detector. The standard deviation in Table 5 indicates the dispersion of speeds around the mean for each simulation scenario, indicating the variability of data within a single run. For example, the higher standard deviation value in sim_4 for SD_07 (approximately 10.9 km/h) suggests greater speed diversity, which may reflect more complex driver behavior, but also potential modeling errors. Statistically, high deviation increases the uncertainty of the mean estimate, which is particularly crucial in road safety, where high speed variance can lead to a higher risk of accidents. Confidence intervals (95%) estimate the range within which the actual mean speed is likely to lie--narrow intervals (e.g., \(\pm\)1.3 km/h in sim_1) indicate high precision, which strengthens the reliability of the simulation for hazard prediction, although limited to a single run. These measures highlight the stability of the model but emphasize the need for multiple replications to achieve full statistical validation. To assess the statistical significance of differences in average speeds across individual simulation scenarios, Student's \(t\)-tests for independent samples ([PERSON]'s \(t\)-test) were performed, assuming unequal variances.