## 4 Experimental Results and Discussion
### Results and Discussion
#### 4.3.2 Prediction Success Rate  
In the experiment, each subject was assigned to do the given task four times with respect to gestures, and each subject performed 27 interactions for each task using pinch or grab. Each task consisted of only grab or only pinch. Each subject conducted four grab tasks and four pinch tasks. Additionally, virtual objects were generated only one time in the same position in one task. Therefore, subjects performed interactions with virtual objects at 27 positions for one task. The number of prediction successes for the entire task is shown in Tables 10 and 11.  
Table 10 shows the number of prediction successes measured in the task for grab. As a result of a calculation based on Table 10, in the grab case, the mean and the standard deviation were 21.25 and 3.40, respectively, and the average prediction success rate was 78.70%.  
\begin{table}
\begin{tabular}{c c c c c c c c} \hline \hline \multirow{2}{*}{**Trial No.**} & \multicolumn{6}{c}{**No. of Successful Predictions**} \\ \cline{2-7}  & **Subject 1** & **Subject 2** & **Subject 3** & **Subject 4** & **Subject 5** & **Subject 6** & **Subject 7** \\ \hline \(1\) & 24 & 21 & 15 & 22 & 18 & 23 & 17 \\ \(2\) & 25 & 23 & 20 & 25 & 14 & 20 & 16 \\ \(3\) & 25 & 21 & 21 & 26 & 19 & 22 & 20 \\ \(4\) & 26 & 25 & 24 & 23 & 18 & 24 & 18 \\ \hline \hline \end{tabular}
\end{table}
Table 10: Number of prediction successes: grab.  
\begin{table}
\begin{tabular}{c c c c c c c} \hline \hline \multirow{2}{*}{**Trial No.**} & \multicolumn{6}{c}{**No. of Successful Predictions**} \\ \cline{2-7}  & **Subject 1** & **Subject 2** & **Subject 3** & **Subject 4** & **Subject 5** & **Subject 6** & **Subject 7** \\ \hline \(1\) & 26 & 22 & 24 & 12 & 27 & 20 & 27 \\ \(2\) & 26 & 13 & 26 & 23 & 27 & 26 & 27 \\ \(3\) & 25 & 19 & 23 & 27 & 26 & 23 & 27 \\ \(4\) & 25 & 19 & 27 & 25 & 27 & 24 & 27 \\ \hline \hline \end{tabular}
\end{table}
Table 11: Number of prediction successes: pinch.  
\begin{table}
\begin{tabular}{c c c c c c} \hline \hline  & **Sum of Squares** & **df** & **Mean Square** & **F** & **Sig.** \\ \hline Between Groups & 0.002 & 2 & 0.000 & 0.017 & 0.984 \\ Within Groups & 0.252 & 18 & 0.014 & & \\ Total & 0.252 & 20 & & & \\ \hline \hline \end{tabular}
\end{table}
Table 9: Results of one-way ANOVA with the \(k\) value as 3, 5, and 7 (prediction success rate of pinch gesture for each subject).  
Table 11 shows the number of prediction successes measured in the task for pinch. As a result of a calculation based on Table 11, in the grab case, the mean and the standard deviation were 23.93 and 4.04, respectively, and the average prediction success rate was 88.62%. Figure 10 shows the average number of interaction prediction successes with respect to subject for each gesture.  
Although sufficient explanation was given before the experiment, there were cases in which the subjects performed wrong actions: a pinch or a none gesture in a grab task, or a grab or a none gesture in a pinch task. To properly evaluate the proposed method, we needed to confirm not only the prediction success rate, but also false positives and false negatives. Therefore, we reviewed all cases to check how often the algorithm produces false positives and false negatives. For this, we compared the subjects' real action data to the prediction results of the proposed method. The result is shown in Tables 12 and 13.