# Comparison of Gait Smoothness Metrics in Healthy Elderly and Young People
## 3 Results  
The average walking velocities observed within the older group displayed minimal variance between self-selected normal walking speed and the instructed faster pace. Specifically, during normal walking, the mean velocity recorded for the older individuals was 0.78 \(\pm\) 0.10 m/s, whereas the average speed increased marginally to 0.97 \(\pm\) 0.16 m/s during the faster walking condition. Conversely, among the younger individuals, there was a considerable contrast in velocities between the two gait conditions. The average speed during normal walking registered at 1.41 \(\pm\) 0.28 m/s, contrasting notably with the faster gait condition where the mean speed increased to 1.96 \(\pm\) 0.24 m/s. This marked discrepancy underscores the substantial difference in velocities exhibited by the younger cohort between the two walking tasks. The velocities of the two walking tasks for both groups are collected in Table 2.  
The comparison of smoothness data between young and older subjects at different walking speeds is presented in Tables 3-5. Table 3 outlines the smoothness values computed using the LDLJ metric and provides insights into statistical differences. It includes _p_-values depicting comparisons between young and older individuals (row-wise) as well as between different walking velocities within each group (column-wise) for every analyzed signal. Similarly, Table 4 showcases analogous comparisons concerning the SPARC metric, while Table 5 focuses on the HR metric. These tables offer a comprehensive overview of the significant differences observed across age groups and walking velocities for each smoothness metric. \begin{table}
\begin{tabular}{c c c} \hline \hline  & **Young** & **Older** \\ \hline Normal (m/s) & 1.41 (0.28) & 0.78 (0.10) \\ Fast (m/s) & 1.96 (0.24) & 0.97 (0.16) \\ \hline \hline \end{tabular}
\end{table} 
Table 2: Averaged gait speed for young and older groups. Values are expressed as mean (standard deviation). \begin{table}
\begin{tabular}{c c c c c} \hline \hline
**LDLJ** & \multicolumn{2}{c}{**Young**} & **Older** \\ \hline \multirow{3}{*}{Acc-V} & Normal & \(-7.41\) (0.95) & \(-9.27\) (0.52) & _p_**\textless{} 0.0001** \\  & Fast & \(-10.26\) (1.02) & \(-8.90\) (0.59) & _p_**\textless{} 0.0001** \\  & & _p_**\textless{} 0.0001** & _p_**\textless{} 0.0001** & \\ \hline \multirow{3}{*}{Acc-ML} & Normal & \(-9.42\) (1.10) & \(-11.81\) (0.53) & _p_**\textless{} 0.0001** \\  & Fast & \(-11.96\) (0.39) & \(-10.97\) (0.46) & _p_**\textless{} 0.0001** \\  & & _p_**\textless{} 0.0001** & _p_**\textless{} 0.0001** & \\ \hline \multirow{3}{*}{Acc-AP} & Normal & \(-8.90\) (1.07) & \(-11.97\) (0.97) & _p_**\textless{} 0.0001** \\  & Fast & \(-11.83\) (0.40) & \(-11.03\) (0.85) & _p_**\textless{} 0.0001** \\  & & _p_**\textless{} 0.0001** & _p_**\textless{} 0.0001** & \\ \hline \hline \end{tabular}
\end{table} 
Table 3: Smoothness of gait calculated through LDLJ for the two age groups at two different speeds with the respective statistical difference _p_-values. _p_-values reported below the group column refer to intra-group comparison, while _p_-values reported on the right column refer to inter-group comparison. Values are expressed as mean (standard deviation).