## 6 Study Analysis and Results
### Treatable Crashes  
The last analysis in the evaluation of the proposed method involved the use of the number of treatable crashes (calculated for five years: 2016-2020) as the performance measure. Treatable crashes are defined as those crashes that may be treated by engineering  
Figure 5: Percent deviation comparison using proposed method, EB method, and PSI method versus crash history: (**a**) crash density-based analysis; (**b**) crash frequency-based analysis.  
countermeasures such as lane widening. The remaining crashes constitute what might be expected due to traffic exposure and may not be treatable by engineering countermeasures. A reasonable estimate for the number of treatable crashes at a location is the number of crashes in excess of what would normally be expected at locations with similar characteristics and traffic exposure [29]. To assess the degree of similarity between the segments identified by a method and those identified by the crash history, a segment overlap metric was used. The higher the percentage of segment overlap and the closer the estimate of treatable crashes with crash history, the better the performance of the compared method.  
Table 4 shows the summary of the estimate of treatable crashes for the proposed method the EB method, and crash history. The table also provides the ratio and overlap for treatable crashes in the top 100 segments defined earlier using both crash density and crash frequency.  
The table shows that, based on crash density, the proposed method identified a fewer number of treatable crashes for the top 100 segments compared to crash history (469 versus 726, respectively). The segment overlap was 66%. Using crash frequency, the segment overlap increased to 79% indicating a significant improvement in performance. Regarding the EB method, the number of treatable crashes and overlap indicate a higher level of consistency with crash history. However, the discrepancy in performance between the proposed and the EB methods is less evident when crash frequency is used in the analysis. Specifically, there were only 11.6% fewer treatable crashes on the segments identified with the proposed method than those identified with the crash history, compared to 11.3% fewer treatable crashes using the EB method. Further, 79% of all segments identified by the proposed method were also on the top 100 segments list of the observed crash.  
In addition to evaluating the top 100 segments identified by the methods, similar calculations were performed for other possible levels of selection up to upper tails having positive treatable crashes. Plots of the treatable crashes identified at various levels are shown in Figure 6. For the range of top segments studied, the chart shows relatively close lines for the proposed and the EB methods, with the EB method consistently identifying a slightly higher number of treatable crashes. The figure also suggests that the larger the total segments selected, the closer the proposed method is in terms of selection efficiency compared to that of EB method. These patterns are similar for the crash density and crash frequency analyses.  
\begin{table}
\begin{tabular}{c c c c c} \hline \hline \multirow{2}{*}{**Methods**} & \multirow{2}{*}{**Total Length (mi)**} & \multirow{2}{*}{**Total Crashes (2016–2020)**} & \multicolumn{2}{c}{**Treatable Crashes (2016–2020)**} \\ \cline{3-5}  & & & **Estimate** & **Overlap** \\ \hline \multicolumn{5}{c}{**Crash Density-Based Analysis**} \\ \hline Proposed Method & 260.55 & 565 & 469 & 66\% \\ EB & 265 & 614 & 522 & 81\% \\ Crash History & 241.1 & 805 & 726 & - \\ \multicolumn{5}{c}{**Crash Frequency-Based Analysis**} \\ \hline Proposed Method & 807.45 & 2220 & 1147 & 79\% \\ EB & 787.05 & 2144 & 1152 & 85\% \\ Crash History & 805.75 & 2439 & 1299 & - \\ \hline \hline \end{tabular}
\end{table}
Table 4: Treatable crashes for the top 100 segments identified.