# Differences Evaluation of Pavement Roughness Distribution Based on Light Detection and Ranging Data
## 4 Lateral Distribution Evaluation of the Pavement Roughness
### Difference Test for the Lateral Distribution of Pavement Roughness
The KW test is a widely employed non-parametric test method that is used to assess differences among multiple independent samples of continuous data. Unlike the ANOVA test, which primarily focuses on determining whether the means of different distributions are equal, the KW test emphasizes the ranking of multiple independent samples and their collective contribution to the overall sample. As a result, the KW test provides a superior evaluation of the inherent variability within the distributions. The KW test statistics are shown in Formulas (15)-(17):  
\[KW_{c}=KW/C \tag{15}\]  
\[KW=\frac{12}{n(n+1)}\cdot\sum_{i=1}^{k}\frac{T_{i}^{2}}{n_{i}}-3(n+1) \tag{16}\]  
\[C=1-\frac{\sum\left(\tau_{i}^{3}-\tau_{i}\right)}{n^{3}-n} \tag{17}\]  
where \(T_{i}\) denotes the rank sum of each sample, \(k\) represents the total number of compared data samples, \(n\) indicates the total individual number after mixing the samples, and \(\tau_{i}\) is the number of \(i\)th tied values (ranks with the same value). In this paper, the field test roads were divided into 10 sections by intersections, including the Bao'an Road section, the Boyuan Road section, the Cao'an Road section, the Jiasong North Road section, the Lianqun Road section, the Lvhuan Road section, the Lvyuan Road section, the Xiangfang Road section, the Yining Road section, and the Zhongbai Road section, respectively. The roughness values of the different survey lines were extracted at intervals of \(l\) = 0.1 m, 0.5 m, 1.0 m, 1.5 m, 2.0 m, 2.5 m, and 3.0 m, respectively. The KW test results are shown in Table 3. \begin{table}
\begin{tabular}{c c} \hline
**Spacing \(l\) (m)** & _p-Value_ \\ \hline
0.1 & 0.2909 \\
0.2 & 0.3487 \\
0.3 & 0.4266 \\
0.5 & 0.2556 \\
1.0 & 0.4356 \\
1.5 & 0.2027 \\
2.0 & 0.9469 \\
2.5 & 0.0311 \\ \hline \end{tabular}
\end{table} 
Table 2: ANOVA test results of the pavement roughness distribution under different survey line spacings. As illustrated in Table 3, the IRI results of various survey lines within one road section were found to be significantly influenced by the road characteristics. Specifically, the Bao'an Highway section exhibited \(p\)-values below 0.05 for all spacing intervals, which indicates substantial differences in the roughness distribution among multiple survey lines. Conversely, the Cao'an Highway section and the Lianqun Road section displayed \(p\)-values above 0.05 across all spacing intervals, suggesting no significant differences in their roughness distribution. In addition, notable variations in \(p\)-values were observed for different spacing intervals, suggesting that the IRI distribution was influenced by the spacing \(l\) between the survey lines in most road sections. Furthermore, the analysis included the examination of the IRI distribution along the centerline of each road section and its correlation with the roughness results. Figure 11 indicates that road sections with a higher substantial dispersion of roughness, such as the Bao'an Highway section, the Lvyuan Road section, and the Jiasong North Road section, exhibited a higher likelihood of significant differences in the roughness results. Conversely, road sections with lower dispersion of roughness, such as the Boyuan Road section and the Cao'an Highway section, showed a relatively low probability of significant differences in the roughness results. This observation can be attributed to the fact that roads with a strong IRI dispersion undergo frequent maintenance and repair activities, leading to changes in their material and structural properties. Consequently, there is an increased likelihood of significant variations in their lateral distribution characteristics.