## 3 Results
Figure 2: Ensemble-averaged curves of the COM–COP inclination angle (IA) and rate of change of IA (RCIA) in the sagittal plane during level walking in patients with lumbar spondylosis (solid line), and healthy controls (dashed line). In the frontal plane, compared to the control, the patients showed increased ranges of IA (\(p<0.05\), Figure 3 and Table 2) with increased time-averaged medial RCIA during SLS, and unaltered IA with increased ranges of RCIA during DLS (\(p<0.05\), Figure 2 and Table 3). The patients showed a strong negative correlation between IA at HS and ACOP during quiet standing (\(p<0.05\), Table 5). The patients also showed a strong positive correlation between the ranges of RCIA during DLS and ACOP during quiet standing (\(p<0.05\), Table 5). \begin{table}
\begin{tabular}{c c c c c} \hline \hline  & **DCOP** & \(p\)**-Value** & **ACOP** & \(p\)**-Value** \\ \hline \multicolumn{5}{c}{**Sagittal Plane**} \\ HS & \(0.35\) & \(0.297\) & \(-0.47\) & \(0.142\) \\ TO & \(-0.66\) & \(0.027\)\({}^{*}\) & \(0.43\) & \(0.193\) \\ Time-averaged values & & & & \\ DLS & \(-0.63\) & \(0.038\)\({}^{*}\) & \(-0.08\) & \(0.819\) \\ SLS & \(-0.61\) & \(0.048\)\({}^{*}\) & \(0.53\) & \(0.094\) \\ Ranges & & & & \\ DLS & \(0.67\) & \(0.024\)\({}^{*}\) & \(-0.46\) & \(0.158\) \\ SLS & \(0.46\) & \(0.157\) & \(-0.73\) & \(0.011\)\({}^{*}\) \\
**Frontal Plane** & & & & \\ HS & \(-0.08\) & \(0.820\) & \(-0.69\) & \(0.019\)\({}^{*}\) \\ TO & \(0.02\) & \(0.961\) & \(-0.40\) & \(0.222\) \\ Time-averaged & & & & \\ DLS & \(0.37\) & \(0.263\) & \(0.10\) & \(0.762\) \\ SLS & \(-0.01\) & \(0.980\) & \(0.28\) & \(0.397\) \\ Ranges & & & & \\ DLS & \(0.12\) & \(0.725\) & \(0.55\) & \(0.078\) \\ SLS & \(0.33\) & \(0.320\) & \(0.43\) & \(0.182\) \\ \hline \hline \end{tabular}
\end{table} 
Table 4: [PERSON]’s correlation coefficient (r) between IA during gait, COP total distance (DCOP), and sway area (ACOP) during quiet standing in the lumbar spondylis group (LS). HS: heel-strike; TO: toe-off; DLS: double-limb support; SLS: single-limb support; \({}^{*}\): significant correlation (\(p<0.05\)). \begin{table}
\begin{tabular}{c c c c} \hline \hline  & \multicolumn{4}{c}{**COM-COP Inclination Angle (RCIA, \({}^{\circ}\)/s)**} \\ \hline
**Variables** & **LS** & **Control** & \(p\)**-Value** \\ \hline \multicolumn{5}{c}{Sagittal Plane: Anterior (+)/Posterior (\(-\))} \\ HS & \(-124.7\) (\(57.0\)) & \(-147.7\) (\(64.5\)) & \(0.386\) \\ TO & \(-21.8\) (\(76.6\)) & \(-53.7\) (\(34.1\)) & \(0.221\) \\ Time-averaged values & & & \\ DLS & \(-90.0\) (\(33.0\)) & \(-136.2\) (\(37.7\)) & \(0.006\)\({}^{*}\) \\ Ranges & & & \\ Ranges & & & \\ DLS & \(-90.0\) (\(33.0\)) & \(-136.2\) (\(37.7\)) & \(0.006\)\({}^{*}\) \\ SLS & \(32.6\) (\(8.1\)) & \(40.3\) (\(4.6\)) & \(0.013\)\({}^{*}\) \\ Ranges & & & \\ DLS & \(275.4\) (\(69.8\)) & \(264.9\) (\(105.4\)) & \(0.787\) \\ SLS & \(166.5\) (\(71.2\)) & \(234.5\) (\(66.0\)) & \(0.031\)\({}^{*}\) \\ \hline \hline \end{tabular}
\begin{tabular}{c c c c} \hline \hline  & \multicolumn{4}{c}{Frontal Plane: Medial (+)/Lateral (\(-\))} \\ HS & \(60.0\) (\(23.9\)) & \(65.8\) (\(35.7\)) & \(0.661\) \\ TO & \(-23.8\) (\(32.7\)) & \(-46.3\) (\(51.9\)) & \(0.238\) \\ Time-averaged & & & \\ DLS & \(47.0\) (\(17.5\)) & \(56.8\) (\(14.9\)) & \(0.172\) \\ SLS & \(1.0\) (\(1.2\)) & \(-0.2\) (\(1.3\)) & \(0.037\)\({}^{*}\) \\ Ranges & & & \\ DLS & \(109.3\) (\(29.2\)) & \(69.9\) (\(8.8\)) & \(0.001\)\({}^{*}\) \\ SLS & \(76.1\) (\(41.0\)) & \(99.7\) (\(72.7\)) & \(0.358\) \\ \hline \hline \end{tabular}
\end{table} 
Table 3: Means (standard deviations) of the RCIA during walking in the lumbar spondylis (LS) and healthy control (control) groups. HS: heel-strike; TO: toe-off; DLS: double-limb support; SLS: single-limb support; \({}^{*}\): significant group effect (\(p<0.05\)).