## 5 Results and Discussion
However, both columns demonstrated \"W\" values below 1, implying notable departure from normality. To summarize, the outcomes derived from the Shapiro-Wilk normality test underscored the absence of normal distribution in the expected crashes obtained from the FRA and field-validated inventory datasets, when FRA's 2020 Accident Prediction (AP) model was applied. Given the absence of normality in expected crashes, a non-parametric statistical approach was chosen to compare dataset disparities. The Wilcoxon rank-sum test, a variant of the Mann-Whitney U test, was utilized to address Hypothesis 1 of this research [28]. This non-parametric counterpart to the two-sample \(t\)-test was applied, and the outcomes are presented in Table 4. The results of the test yielded a \(p\)-value below 0.05 and a test statistic (W) of 122,640, strongly indicating differing medians between the distributions. The alternate hypothesis, stipulating a nonzero true location shift, signifies that one population's distribution is asymmetrically positioned relative to the other, implying distinct medians. Due to the non-parametric nature of the data, estimations such as mean values were not calculated. The test's purpose was exclusively to ascertain evidence of distributional shifts between the two datasets. The analysis of crash prediction using field-validated data demonstrated a discrepancy in the hazard rankings of HRGCs compared to rankings derived from FRA's data. Table 5 highlights the impact of employing field-validated data instead of the original FRA inventory data on HRGCs hazard rankings. This reveals the potential for misallocating \begin{table}
\begin{tabular}{l l l} \hline \hline
**Tests Performed** & & \\ \hline Shapiro–Wilk Normality Test & & \\ Variable & W & \(p\)-value \\ Original FRA data crash & 0.87519 & \(2.2\times 10^{-16}\) \\ predictions & 0.84692 & \(2.2\times 10^{-16}\) \\ \hline Wilcoxon Rank Sum Test for Differences in Expected Crashes & & \\ Original FRA Vs FV data & 122,640 & \(3.622\times 10^{-10}\) \\ crash predictions & True location shift is not equal to 0 & \\ \hline \hline \end{tabular}
\end{table} 
Table 4: Statistical testing of normality and disparities in expected crashes [2]. safety resources for HRGCs when an incomplete dataset is utilized for predictive modeling. For instance, a specific HRGC labeled as \"074929T\" is ranked third in terms of crash hazard when assessed with field-validated data but drops to fifth when using the original FRA data for crash prediction. Moreover, several crossings that ranked within the top-10 hazards in the FRA dataset do not maintain their top-10 rankings when evaluated using the field-validated dataset. This information underscores the significance of accurate inventory data; its absence could lead to oversight by agencies in allocating resources for crossings with actual high crash risks. Flawed ranking based on the current FRA datasets might result in the exclusion of crossings that warrant risk mitigation interventions. The second hypothesis of the research aimed to assess differences in estimated parameters and models' performance based on the FRA and field-validated dataset. Also, it was studied to see if estimated coefficients are statistically significantly different in the two estimated Zero-inflated Negative Binomial (ZINB) models. Estimation of the base and comparison models using 5-year crashes (2017-2021) reported at the 560 HRGCs (finally reduced to N = 555) showed that the model based on the field-validated data gave a different expected magnitude of regressors when compared to the base model. However, it was yet to be determined if these differences were statistically significant. Table 6 presents the estimated base ZINB model that utilized the original FRA HRGCs inventory data (Table 3 provides variable coding). Table 7 presents the estimated comparison model based on field-validated inventory data (Table 3 provides variable coding). Tables 6 and 7 also present the performance indicators for base and comparison ZINB models.