## 3 Results  
Table 4 contains data about the time synchronization of upper body kinematical variables (Gaze Yaw, Head Yaw, Trunk Yaw, Trunk Roll). Additionally, we included available data about the \begin{table}
\begin{tabular}{c c c c} \hline  & **Time Delay (ms)** & **Standard Error** & **Reference** \\ \hline \hline \multirow{2}{*}{GY} & 40 \(\pm\) 371 & & [26] \\  & 326 \(\pm\) 237 & & [26] \\ \multirow{2}{*}{HY} & 180 \(\pm\) 164 & 30 & [23] \\  & 530 \(\pm\) 164 & 30 & [23] \\  & 360 \(\pm\) 100 & 10 & [24] \\  & 530 \(\pm\) 250 & 25 & [25] \\  & \(-\)734 \(\pm\) 1518 & 160 & [28] \\  & 50 \(\pm\) 317 & & [26] \\ \multirow{2}{*}{TY} & 349 \(\pm\) 210 & & [26] \\  & 470 \(\pm\) 164 & 30 & [23] \\  & 700 \(\pm\) 164 & 30 & [23] \\  & 420 \(\pm\) 100 & 10 & [24] \\  & 610 \(\pm\) 200 & 20 & [25] \\  & \(-\)571 \(\pm\) 1518 & 160 & [28] \\ \multirow{2}{*}{TR} & 280 \(\pm\) 164 & 30 & [23] \\  & 390 \(\pm\) 164 & 30 & [23] \\  & 500 \(\pm\) 300 & 30 & [24] \\ \multirow{2}{*}{MLC} & \(-\)177 \(\pm\) 1518 & 160 & [28] \\  & 610 \(\pm\) 380 & 38 & [24] \\ \multirow{2}{*}{700 \(\pm\) 200} & 20 & [25] \\  & \(-\)447 \(\pm\) 1138 & 120 & [28] \\ \hline \hline \end{tabular}
\end{table} 
Table 3: Time delays (mean \(\pm\) standard deviation) from a reference event in a preparatory step to turn onsets on different variables (GY, HY, TY, TR, MLC) collected from references specified in Column 4. When not provided in the original paper, the standard deviation was estimated from the reported standard error (Column 3) using the number of users and trials involved in the experiments as reported in Table 2-Column 2.  
anticipation time of each variable with respect to the estimated body Trajectory Heading (TJH) and the Medio-Lateral COM displacement (MLC). Values in bold were directly reported in the corresponding reference. The others were calculated by combining results from Table 3 as described in Section 2.5. An aggregated analysis reveals that Gaze Yaw significantly anticipates Head Yaw by 179 ms (\(p\)-value \(<\) 0.01). The 95% confidence interval for the anticipation is [54 ms, 305 ms]. However, the shortest value (10 \(\pm\) 195 ms) reported in [26] could be explained by the nature of sudden turn decisions which just made subjects re-orient segments faster, as they were told the direction to turn using a visual cue that was emitted at the turning point. Therefore, if we consider only the remaining experiments, where subjects were informed at the beginning of the experiment about the turn to take, and hence, had enough time in advance to schedule the turning maneuver, the combined analysis reveals that Gaze Yaw significantly anticipates Head Yaw by 198 ms (\(p\)-value \(<\) 0.01, 95% confidence interval [68 ms, 327 ms]). Head Yaw significantly anticipated Trunk Yaw by 149 ms (\(p\)-value \(<\) 0.01, 95% confidence interval [47 ms, 251 ms]). As before, some results (170 \(\pm\) 90 ms, 60 \(\pm\) 55 ms, 80 \(\pm\) 132 ms, reported in [23; 24; 25]) were obtained from experiments where users had to turn immediately after a signal/auditive clue. Excluding these results, Head Yaw significantly anticipated Trunk Yaw by 271 ms (\(p\)-value \(<\) 0.001, 95% confidence interval [117 ms, 424 ms]). On the other side, Head Yaw significantly anticipated Trajectory Heading by 241 ms (\(p\)-value \(<\) 0.05, 95% confidence interval [37 ms, 445 ms]). Conversely, Head Yaw was not significantly different from Trunk Roll (mean anticipation 11 ms, 95% confidence interval [\(-\)178 ms, 200 ms]), nor from Medio-Lateral COM Displacement (mean anticipation 185 ms, 95% confidence interval [\(-\)49 ms, 420 ms]). Trunk Yaw did not significantly anticipate Medio-Lateral COM Displacement (mean anticipation 102 ms, 95% confidence interval [\(-\)98 ms, 302 ms]). Finally, Trunk Roll significantly anticipated Trunk Yaw by 216 ms (\(p\)-value \(<\) 0.01, 95% confidence interval [84 ms, 348 ms]). Trunk Roll did not significantly anticipate Medio-Lateral COM Displacement (mean anticipation 88 ms, 95% confidence interval [\(-\)295 ms, 471 ms]).