## 5 Results and Discussion  
Crash predictions (expected crashes) based on the FRA's 2020 Accident Prediction (AP) model (by utilizing the two different datasets) yielded disparate results. To gain a deeper comprehension of the magnitude of these disparities, the percentage differences were computed and plotted. As depicted in Figure 7, a noticeable distinction is evident in the expected crash values obtained from the two inventory datasets. The figure illustrates the percentage variations between the FRA and field-validated (FV) data's crash predictions. It is evident from the data that the percentage differences range from 0 to over 140%, suggesting that the anticipated crash counts could be nearly double or half of the actual crash count. Additionally, Figure 7 also shows that the majority of HRGCs demonstrated expected crash values within a 0-20% range of difference. However, a higher percentage difference in expected crashes was only observed in 7 HRGCs (1.25% of the total HRGCs). \begin{table}
\begin{tabular}{c c} \hline \hline
**Variables** & **Variable Coding** \\ \hline Discrete Variables & \\ Warning flashing lights & 1 if there are flashing lights at crossing, 0 otherwise \\ Gates & 1 if there are gates at crossing, 0 otherwise \\ Rural/urban classification & 1 if crossing is in urban area, 0 if crossing is in rural area \\ Pavement markings & 1 if there are pavement markings near crossing, 0 otherwise \\  & Timber = 1, Asphalt = 2, Asphalt and Timber or \\ Crossing surface type & Concrete or Rubber = 3, Concrete and \\  & Rubber = 4, other = 5 \\ Crossing illuminated & 1 if crossing is illuminated, 0 otherwise \\ Crossing angle & 1 = 0–29\({}^{\circ}\), 2 = 30–59\({}^{\circ}\), 3 = 60–90\({}^{\circ}\) \\ Continuous Variables & \\ Number of bells & Count \\ Number of crossbucks & Count \\ Number of total tracks & Count \\ Ln AADT & Natural Log-transformed count \\ Ln Total daily trains & Natural Log-transformed count \\ Ln Maximum timetable speed & Natural Log-transformed count \\ Number of traffic lanes & Count \\ \hline \hline \end{tabular}
\end{table} 
Table 3: Candidate variables for inclusion in base and comparison crash prediction models [2]. Figure 7: Comparison of expected crashes: FRA vs. field-validated data [2]. To conduct the first hypothesis test in this research, we examined whether the crash predictions estimated from the utilization of two datasets conform to a normal distribution. This initial step was crucial to guarantee the correct application of hypothesis tests. To assess the normality of predicted crashes using FRA and field-validated data, the Shapiro-Wilk test was employed, offering a formal determination of data normality (Ho = data distribution is normal, at \(\alpha=5\%\)) [27; 28]. A \(p\)-value below 0.05 during the Shapiro-Wilk test suggests non-normal distribution in at least one data column (expected crashes). In such instances, non-parametric tests are viable for dataset comparisons, such as the Wilcoxon rank-sum test (Mann-Whitney U test) or Kruskal-Wallis test [27; 28]. These alternatives, unlike \(t\)-tests or ANOVA, are robust against non-normality assumptions, offering reliable options when normality criteria are not met. The null hypothesis under examination through the Shapiro-Wilk normality test (Table 4) posited non-conformance of the data with a normal distribution. The test yielded a computed test statistic denoted as \"W\", accompanied by its corresponding \"\(p\)-value\". In the context of projected collision incidents drawn from two distinct datasets, the observed \"\(p\)-value\" exhibited a significance level below 0.05, indicative of compelling contradiction against the null hypothesis. Consequently, substantial support emerged to refute the assumption of normal distribution in the data. The values of \"W\", representing the test statistic, for both data columns (pertaining to anticipated collision incidents) were confined within the interval of 0 to 1. The proximity of \"W\" to 1 corresponded to increased adherence to normality.