# Movement Time for Pointing Tasks in Real and Augmented Reality Environments
## 4 Discussion
### Information Processing Performance  
The inverse of the regression coefficient \(b\) in [PERSON]'s law equation was adopted to indicate the information processing rate of the hand movement performing the pointing task [52]. The literature has shown that the information processing rate for arm movements was approximately 10 bit/s [25; 53]. The inverse of \(b\) (or \(1/b\)) in Table 4 for horizontal and vertical pointing tasks was between 6.9 bit/s and 7.4 bit/s and between 13.4 bit/s and 15.9 bit/s, respectively. The former was approximately half of the latter, indicating that horizontal pointing was less efficient than vertical pointing. It was anticipated that the information processing rate for the virtual pointing tasks should be different from that of the physical ones. However, the \(1/b\) values of these two types of tasks in Table 4 were confounded because \(T\) was incorporated in ID\({}_{\text{adj}}\). Therefore, the inverse of \(b\) could not accurately represent the information processing rate when the ID was adjusted with factors in addition to movement distance and target size. [PERSON] [54] also indicated that \(1/b\) cannot be used to quantify the information transfer because of the wavering influence of the intercept \(a\) and the inconsistency between \(1/b\) and [PERSON]'s original definition of index of performance, or throughput. We then calculated the throughput (TP) using the following equation:  
\[\text{TP}=\frac{ID_{adj}}{MT}. \tag{9}\]  
Table 5 shows the TP for the pointing tasks. The TP values for the physical pointing tasks were between 11.6 and 12.6 bit/s for both the horizontal and vertical movements and were relatively stable. They were between 8.8 and 9.8 bit/s for horizontal or virtual-horizontal pointing tasks and were significantly (\(p<0.001\)) lower than those of the physical-horizontal tasks. On the contrary, the TP values of the virtual-horizontal pointing tasks were between 12.2 and 15.0 bit/s and were significantly (\(p<0.001\)) higher than those of the physical tasks in the same direction. This implies that the information processing performance between pointing at physical and virtual panels was dependent on the hand movement direction. The participants had inferior information processing performance when pointing at virtual targets than that on physical targets if they were pointing laterally. On the contrary, they had better performance when pointing at virtual targets than on physical targets if they were pointing in the top-down direction. This might be attributed to the fact that the top-down pointing movements involved less movement of the shoulder joint than the lateral pointing movements. It was also likely that the visual depth deficiency problems in the top-down movements were less prominent than in the lateral direction.  
\begin{table}
\begin{tabular}{c c c c c} \hline \hline
**Movement Direction** & **Gender** & **Hand** & **Physical Pointing** & **Virtual Pointing** \\ \hline Horizontal & Female & D & 11.75 & 8.94 \\ \hline  & ND & 11.15 & 8.84 \\ \hline  & Male & D & 12.54 & 9.76 \\ \hline  & ND & 11.9 & 9.4 \\ \hline Vertical & Female & D & 11.6 & 13.17 \\ \hline  & ND & 11.29 & 12.22 \\ \hline  & Male & D & 12.55 & 14.98 \\ \hline  & ND & 11.9 & 14.09 \\ \hline \hline \end{tabular}
\end{table}
Table 5: Throughput (bit/s) for the pointing tasks.