## 6 Study Analysis and Results
### True Positive Identification  
Secondly, the identification of true positive segments is calculated. A true positive occurs when the proposed method correctly identifies a segment as a potential for safety improvement. This evaluation listed the number and percentage of common segments between two lists: the one compiled using ranks from the proposed method and the other using ranks from observed crash data. The higher the number and percentage of the common sites, the better the performance of the subject method because this indicates a stronger agreement between the prediction of the proposed method and crash history.  
Table 3 shows a comparison of the identification of true positive segments by three different methods--the proposed method, the Empirical Bayes (EB) method, and the PSI method--while using observed crash data as a reference in the context of crash density and crash frequency analysis for various upper tail segments.  
When evaluating the identification of common segments using crash density, for upper tail segments (20), the proposed method was least consistent with crash history (30%), followed by the EB method (65%) and the PSI method (90%), respectively. With the increase in upper tail segments, the discrepancy between the proposed method and the EB and PSI methods decreases. However, the performance of the proposed method is overall less favorable compared to that of the other two methods. For example, in upper tail segments (100), the proposed method identified 68 sites versus 78 sites for the EB method and 87 sites for the PSI method.  
When using crash frequency in the analysis, show better performance for the proposed method and lower discrepancy between the three methods. For instance, the proposed method identified 78% of true positive segments compared to 86% by the EB method and 88% by the PSI method when considering 100 upper tail segments. Further, for every other  
\begin{table}
\begin{tabular}{c c c c c c c c} \hline \hline \multirow{2}{*}{**Groups**} & \multirow{2}{*}{**\% of Segments**} & \multicolumn{4}{c}{**Number of Common Segments**} & \multicolumn{4}{c}{**\% of Common Segments**} \\ \cline{3-8}  & & **Proposed Method** & **EB Method** & **PSD Method** & **PSD Method** & **PSD Method** \\ \hline \multicolumn{8}{c}{**Crash Density Analysis**} \\ \hline Upper Tail (20) & 5.31\% & 6 & 13 & 18 & 30 & 65 & 90 \\ \hline Upper Tail (40) & 10.61\% & 22 & 31 & 37 & 55 & 77.5 & 92.5 \\ \hline Upper Tail (60) & 15.92\% & 30 & 45 & 51 & 50 & 75 & 85 \\ \hline Upper Tail (80) & 21.22\% & 46 & 60 & 64 & 57.5 & 75 & 80 \\ \hline Upper Tail (100) & 26.53\% & 68 & 78 & 87 & 68 & 78 & 87 \\ \multicolumn{8}{c}{**Crash Frequency Analysis**} \\ \hline Upper Tail (20) & 5.31\% & 12 & 17 & 17 & 60 & 85 & 85 \\ \hline Upper Tail (40) & 10.61\% & 30 & 34 & 34 & 75 & 85 & 85 \\ \hline Upper Tail (60) & 15.92\% & 41 & 49 & 50 & 68.33 & 81.67 & 83.33 \\ \hline Upper Tail (80) & 21.22\% & 61 & 68 & 70 & 76.25 & 85 & 87.5 \\ \hline Upper Tail (100) & 26.53\% & 78 & 86 & 88 & 78 & 86 & 88 \\ \hline \hline \end{tabular}
\end{table}
Table 3: True positive segment identification comparison for proposed method versus the EB method versus the PSI method.  
upper tail considered, the results from the proposed method shows lower discrepancy with those using the other two methods.