# Arm Posture Changes and Influences on Hand Controller Interaction Evaluation in Virtual Reality
## 5 Results  
### Target Acquisition Error Rate  
Using the error times that were recorded in task log files, we calculated error rates in percentage (%). For example, there were a total of forty-eight error times recorded at the horizontal angle of 0\({}^{\circ}\) at the shoulder height in 90 log files (30 participants \(\times\) 3 hand-operational distances) of the left-hand interaction; the error rate of the left-hand acquisition at this position was 48/(90 \(\times\) 10) = 0.0533. Table 2 presents a summary of error rate statistical results. \begin{table}
\begin{tabular}{l l} \hline \multicolumn{2}{c}{**Independent Variables**} \\ \hline
1. Hand-use choice & Left; \\  & Right; \\ \hline
2. Arm-bending degree: & Wholly-bent: 30 cm; \\  & Half-bent: 45 cm; \\  & Stretched: 60 cm; \\ \hline
3. Hand-operational position & Horizontal angles (5): \(-90^{\circ}\), \(-45^{\circ}\), \(0^{\circ}\), \(45^{\circ}\), \(90^{\circ}\); \\  & Vertical heights (3): overhead, shoulder, waist; \\ \hline \end{tabular}
\end{table} 
Table 1: A summary of the independent variables in experiment. Figure 5 visualizes the target acquisition error rates at distinct horizontal angles by left and right hands. In the left-hand interactions, it can be observed that target acquisition error rates on the left side (at angles of \(-90^{\circ}\) and \(-45^{\circ}\)) were significantly lower than those on the right side (at angles of \(45^{\circ}\) and \(90^{\circ}\)); however, in the right-hand interactions, the result was converse. By comparing the error rates of the left-hand interactions and the right-hand interactions, no significant difference was found (\(t(1349)=0.36\), \(p=0.63\)). This indicates that the user-preferred or dominant hand has no advantage in interaction accuracy than the non-dominant hand. A repeated-measured ANOVA of _Hand-use choice_\(\times\)_Arm-bending degree_ showed that the effect of the _Hand-use choice_ is not significant (F(1, 14) = 0.47, \(p=0.505\)), indicating that \begin{table}
\begin{tabular}{c c c c c c c c} \hline \hline \multirow{2}{*}{**Hand Use**} & \multirow{2}{*}{**Arm-Bending**} & \multirow{2}{*}{**Hand-Operational**} & \multicolumn{6}{c}{**Acquisition Error Rate at Horizontal Angles**} \\ \cline{3-8}  & & & & \(-\)**90\({}^{\circ}\)** & \(-\)**45\({}^{\circ}\)** & **0\({}^{\circ}\)** & **45\({}^{\circ}\)** & **90\({}^{\circ}\)** \\ \hline \multirow{6}{*}{Left hand} & \multirow{3}{*}{Stretched} & Overhead & 0.063 & 0.053 & 0.060 & 0.100 & 0.130 \\  & & Shoulder & 0.067 & 0.043 & 0.057 & 0.083 & 0.117 \\  & & Waist & 0.050 & 0.040 & 0.043 & 0.067 & 0.127 \\ \cline{2-8}  & \multirow{3}{*}{Half-bent} & Overhead & 0.053 & 0.040 & 0.050 & 0.073 & 0.113 \\  & & Shoulder & 0.047 & 0.033 & 0.053 & 0.057 & 0.090 \\  & & Waist & 0.037 & 0.030 & 0.040 & 0.047 & 0.103 \\ \cline{2-8}  & \multirow{3}{*}{Wholly-bent} & Overhead & 0.040 & 0.027 & 0.033 & 0.053 & 0.073 \\  & & Shoulder & 0.033 & 0.023 & 0.030 & 0.047 & 0.070 \\  & & Waist & 0.027 & 0.020 & 0.027 & 0.040 & 0.063 \\ \hline \multirow{6}{*}{Right hand} & \multirow{3}{*}{Stretched} & Overhead & 0.110 & 0.093 & 0.053 & 0.050 & 0.057 \\  & & Shoulder & 0.107 & 0.080 & 0.050 & 0.033 & 0.053 \\  & & Waist & 0.093 & 0.067 & 0.033 & 0.030 & 0.050 \\ \cline{2-8}  & \multirow{3}{*}{Half-bent} & Overhead & 0.100 & 0.063 & 0.047 & 0.037 & 0.050 \\  & & Shoulder & 0.083 & 0.047 & 0.047 & 0.027 & 0.040 \\  & & Waist & 0.097 & 0.040 & 0.030 & 0.023 & 0.047 \\ \cline{2-8}  & \multirow{3}{*}{Wholly-bent} & Overhead & 0.070 & 0.047 & 0.030 & 0.023 & 0.033 \\  & & Shoulder & 0.067 & 0.040 & 0.027 & 0.027 & 0.030 \\  & & Waist & 0.083 & 0.037 & 0.027 & 0.017 & 0.027 \\ \hline \hline \end{tabular}
\end{table} 
Table 2: Target acquisition error rates at different positions by either hand. Figure 5: Target acquisition error rates at different bending degrees of the arm: (**a**) left-hand interaction result; (**b**) right-hand interaction result.