# Arm Posture Changes and Influences on Hand Controller Interaction Evaluation in Virtual Reality
## 5 Results
### End-Point Scatter  
As previously mentioned, the task log files recorded 3D coordinates of the fifteen target actual positions and the end-points. Using the coordinate records, we calculated the end-point scatter from the target's actual position, as illustrated in Figure 7. The calculation method of the end-point scatter in different directions can be expressed as shown below:  
\[\text{scatter}(x,y,\,z)=\sqrt{\left(x_{2}-x_{1}\right)^{2}+\left(y_{2}-y_{1} \right)^{2}+\left(z_{2}-z_{1}\right)^{2}} \tag{3}\] \begin{table}
\begin{tabular}{c c c c} \hline \hline
**Arm-Bending Degree** & **Mean Error Rate** & **Std. Dev.** & **Post-Hoc Pairwise Comparisons** \\ \hline Stretched & 0.069 & 0.013 & Stretch—Half-bent: \(p<0.05\), [PERSON]’s d = 1.12 \\ Half-bent & 0.055 & 0.011 & Stretch—Wholly-bent: \(p<0.05\), [PERSON]’s d = 2.38 \\ Wholly-bent & 0.040 & 0.009 & Half-bent—Wholly-bent: \(p<0.05\), [PERSON]’s d = 1.48 \\ \hline
**Hand-Operational Height** & **Mean Error Rate** & **Std. Dev.** & **Post-Hoc Pairwise Comparisons** \\ \hline Overhead & 0.061 & 0.011 & Overhead—Shoulder: \(p<0.05\), [PERSON]’s d = 0.64 \\ Shoulder & 0.054 & 0.010 & Overhead—Waist: \(p<0.05\), [PERSON]’s d = 1.04 \\ Waist & 0.049 & 0.012 & Shoulder—Waist: \(p<0.05\), [PERSON]’s d = 0.45 \\ \hline \hline \end{tabular}
\end{table} 
Table 3: Target acquisition error rate in different conditions of the arm-bending degree and the hand-operational height, and pairwise comparisons. Figure 6: Target acquisition error rate at different heights by either hand: (**a**) left-hand interaction result; (**b**) right-hand interaction result. According to Equation (3), the end-point scatter reflected the integrated offset in three directions. We used a visualized diagram to present the end-point scatter result at different positions by either hand, shown in Figure 8. The diameter of the circles reflects the standard deviation of scatters, the center of circles refers to the averaged position of end-points and the black line indicates the offset from the end-points' average position to the target's actual position. A larger circle represents the end-points being more scattered, and the target acquisition being less accurate. Figure 8: End-point scatters at different positions and operational distances: (**a1,a2**) are end-point scatters at a stretched arm posture; (**b1,b2**) are end-point scatters at a half-bent arm posture; (**c1,c2**) are end-point scatters at a wholly-bent arm posture. Figure 7: An illustration about the end-point’s offset or scatter from the target’s actual position. A repeated-measures ANOVA of _Hand-use choice \(\times\) Arm-bending degree \(\times\) Hand-Operational Height \(\times\) Horizontal Angle_ showed that _Hand-use choice_ has no obvious effect on the end-point scatter (\(F(1,\,291)=1.86,\,p=0.137\)), indicating that two hands generate little difference in end-point scatter. Meanwhile, there are significant effects of the _Arm-bending degree_ (\(F(2,\,582)=8.97,\,p<0.05\)), _Hand-Operational Height_ (\(F(2,\,582)=25.48,\,p<0.05\)) and _Horizontal Angle_ (\(F(4,\,1164)=207.16,\,p<0.05\)). There is also a significant interaction effect of _Hand-use choice \(\times\) Hand Horizontal Angle_ (\(F(1,\,291)=51.14,\,p<0.05\)). Table 4 presents the detailed analysis result of the pairwise comparisons. In summary, a stretched arm posture generated a more obvious end-point scatter than a half-bent arm posture. A wholly-bent arm posture generated the least end-point scatter; hand-controller interaction at the waist height resulted in a smaller end-point scatter than that at the shoulder height, but end-point scatter at the overhead height was the most obvious. In left hand-controller interaction, end-point scatters on the right side (at angles of \(45^{\circ}\) and \(90^{\circ}\)) were larger than that on the left side (at angles of \(-45^{\circ}\) and \(-90^{\circ}\)); however, in right hand-controller interaction, the result was converse.