## 3 Results and Discussion
### Hit-the-Ball  
#### 3.2.1 Accuracy-Rate Analysis  
Table 8 shows the accuracy rate and the results of the Kruskal-Wallis test for comparisons of the three groups at different speed levels for accuracy-rate analysis. In the three \begin{table}
\begin{tabular}{c c c c c c} \hline \hline  & \multicolumn{3}{c}{**MMSE**} & \multicolumn{3}{c}{**One-Way ANOVA**} \\ \cline{2-6}
**Game Level** & **Normal (1)** & **MCI (2)** &
\begin{tabular}{c} **Moderate-to-** \\ **Severe (3)** \\ \end{tabular} & **F** & \(p\)**-Value** \\ \cline{2-6}  & **Mean \(\pm\) SD a** & **Mean \(\pm\) SD a** & **Mean \(\pm\) SD a** & **Mean \(\pm\) SD a** & **\\ \hline slow & 1.10 \(\pm\) 0.18 & 1.27 \(\pm\) 0.19 & 1.34 \(\pm\) 0.21 & 5.675 & 0.007 a \\ medium & 1.07 \(\pm\) 0.19 & 1.26 \(\pm\) 0.12 & 1.32 \(\pm\) 0.18 & 7.865 & 0.002 a \\ fast & 0.71 \(\pm\) 0.36 & 0.40 \(\pm\) 0.46 & 0.68 \(\pm\) 0.41 & 3.581 & 0.039 a \\ \hline \hline \end{tabular}  
* SD indicates standard deviation.  
\end{table} 
Table 6: Time-limited mode: the response time(s) of each group of MMSE at different game speeds. \begin{table}
\begin{tabular}{c c c c c c} \hline \hline  & \multicolumn{3}{c}{**MMSE**} & \multicolumn{3}{c}{**One-Way ANOVA**} \\ \cline{2-6}
**Game Level** & **Normal (1)** & **MCI (2)** &
\begin{tabular}{c} **Moderate-to-** \\ **Severe (3)** \\ \end{tabular} & **F** & \(p\)**-Value** \\ \cline{2-6}  & **Mean \(\pm\) SD a** & **Mean \(\pm\) SD a** & **Mean \(\pm\) SD a** & **Mean \(\pm\) SD a** & **\\ \hline slow & 1.13 \(\pm\) 0.19 & 1.29 \(\pm\) 0.24 & 1.34 \(\pm\) 0.21 & 3.637 & 0.037 a \\ medium & 1.08 \(\pm\) 0.20 & 1.28 \(\pm\) 0.15 & 1.38 \(\pm\) 0.19 & 8.792 & 0.001 a \\ fast & 1.05 \(\pm\) 0.17 & 1.23 \(\pm\) 0.16 & 1.31 \(\pm\) 0.16 & 9.114 & 0.001 a \\ \hline \hline \end{tabular}  
* SD indicates standard deviation.  
\end{table} 
Table 7: Time-unlimited mode: posterior comparison of each group of MMSE at different game speeds. groups grouped by MMSE in the time-limited case, the Kruskal-Wallis test was used to observe whether the three groups were different at the three speed levels of the hit-the-ball game. After the posterior test with the Mann-Whitney U test, the results showed that, when the speed is fast, there is a significant difference between the moderate-to-severe group and the normal group (\(p<0.05\)) but there is no significant difference between the moderate-to-severe group and the MCI group (\(p>0.05\)) as well as no significant difference between the normal group and MCI group (\(p>0.05\)). In the time-limited mode, when the game speed is fast, the normal group and the moderate-to-severe group can be distinguished but the normal and MCI groups cannot be distinguished. In Table 8, we can observe that, when the game speed is fast, the performance of those in the normal group and the MCI group is much better than that of those in the moderate-to-severe group. In the time-unlimited mode, the Kruskal-Wallis test was used to observe whether the three groups were different under the three game speed modes. The results showed that the performance of the three groups under the three game speeds was significantly different (\(p<0.05\)). After a posterior comparison with the Mann-Whitney U test, the results show that, when the speed is slow and fast, there is a significant difference between the moderate-to-severe group and the normal group (\(p<0.05\)) as well as a significant difference between the MCI and moderate-to-severe group (\(p<0.05\)); when the speed is medium, there is a significant difference between the normal group and the moderate-to-severe group (\(p<0.05\)). This means that time-unlimited play is relatively simple for the normal group and the MCI group while the moderate-to-severe group will have some difficulties. To determine the judgment abilities of the three groups divided by MMSE, by using the Kruskal-Wallis test to observe whether the three groups are different under the three game speeds, the results showed that there were significant differences in performance (\(p<0.05\)) between the three groups.