# Effect of Target Size, Location, and Input Method on Interaction in Immersive Virtual Reality
## 4 Results
### Target Location  
To investigate the influence of the TCT per the position of the target, the average TCT was obtained for each target position. The one-way repeated measure of ANOVA analysis was performed using the target location as an independent variable (\(\alpha\) = 0.05). The target location data were entered on a nominal scale from 1 to 25 in order from the top left. The result showed that the target position was a significant factor in the TCT in all experimental conditions (\(p\) < 0.001). Post-hoc analysis was performed using the Student-Newman-Keuls (SNK) test, and SNK analysis showed statistically significant differences for the target location (Figure 7).  
We performed a separate classification task to visually check how the TCT differed according to the position of the target. First, TCTs, according to 25 targets, were grouped by post hoc analysis. Among them, the targets belonging to the same group as the target corresponding to the median value were classified into the medium speed group. The targets with shorter times were classified into the fast-speed group based on the medium-speed group, and those with longer times were classified into the slow-speed group. Table 4  
Figure 6: Mean task completion time for each condition. (Circles show no statistically significant difference, and the y-axis does not start at zero).  
Figure 7: Task completion time for target location. (Different letters indicate statistically significant differences, Error bars refer to standard deviation).  
shows the range of TCTs for the three groups determined by the target size and the selection method.  
Figure 8 shows the distribution of TCT for each condition. According to the criteria in Table 4, the slow-speed group was shown in dark gray, the medium-speed group in light gray, and the fast-speed group in white. In all experimental conditions, targets located at the center were classified into the fast-speed group. Additionally, as the distance from the center increased, time also became longer. In particular, targets located farthest from the center were classified into the slow-speed group.  
Unlike the TCT, the chi-squared test found that the target position was not statistically significant at ER (\(p=0.876\); \(\alpha=0.05\)). Figure 9 shows the location of the error in each condition. Errors less than \(1/3\) of all errors were white, less than \(2/3\) errors were light gray, and the rest were dark gray. Thus, the darker the color, the more errors occurred at the position; the brighter the color, the fewer errors occurred. Figure 9a,b show the error distributions for large and small targets. By comparison, whereas the error rate was not analyzed as a significant difference per the target size, more errors occurred in the smaller target. However, through Figure 9c,d, the error distribution of the two selection methods could be checked. In the case of manual selection, many areas were painted in dark colors, but in gaze selection, all areas were marked in white. As with the results of the analysis in Section 4.3, it can be confirmed that errors occurred significantly, depending on the selection method. However, there was no effect from the target position.  
\begin{table}
\begin{tabular}{c c c c} \hline  & **Fast-Speed** & **Medium-Speed** & **Slow-Speed** \\ \hline \multirow{2}{*}{Target size} & Large & Under 2040 & From 2040 to 2560 & Over 2560 \\ \cline{2-2}  & Small & Under 2242 & From 2242 to 2765 \\ \hline \multirow{2}{*}{Input method (B)} & Manual & Under 1977 & From 1977 to 2465 \\ \cline{2-2}  & Gaze & Under 2443 & From 2443 to 2987 \\ \hline \multicolumn{2}{c}{A \(\times\) B} & Under 2100 & From 2100 to 2700 \\ \hline \end{tabular}
\end{table}
Table 4: The range of task completion time according to the size of the target and the input method. (unit: ms).  
Figure 8: The distribution of mean task completion time for each condition: (**a**) large target size; (**b**) small target size; (**c**) manual-selection method; (**d**) gaze-selection method; (**e**) all conditions.