## 4 Results
### Quantitative Data Analysis
#### 4.2.1 Execution Time
The fourth level of the game was designed to test participants' interaction with a virtual 3D surface in different contexts. Each sublevel of this level retains the basic concept of a quiz, but varies in the dimensions and placement of the interactive graphical elements, while the third sublevel adds distracting elements. Table 6 shows the results of the statistical analysis at this level. \begin{table}
\begin{tabular}{l c c c c c c c c c c c} \hline \hline
**Sublevel** & **M** & **C** & **\(\sigma\)** & **min** & **max** & **R** & **Q1** & **Q3** & **IQR** & **S** & **K** \\ \hline Horizontal orientation & 7.06 & 5.98 & 2.99 & 1.86 & 15.20 & 13.34 & 4.79 & 8.92 & 4.13 & 0.84 & 0.11 \\ Vertical orientation & 16.81 & 12.31 & 13.09 & 1.93 & 61.77 & 59.84 & 8.01 & 21.89 & 13.88 & 1.65 & 2.60 \\ Distracting background & 7.24 & 6.55 & 3.39 & 1.01 & 20.38 & 19.37 & 4.90 & 8.58 & 3.67 & 1.48 & 3.56 \\ \hline \hline \end{tabular}
\end{table} 
Table 6: Statistical analysis of the time needed to complete tasks on sublevels of the fourth level. \begin{table}
\begin{tabular}{l c c c c c c c c c c} \hline \hline
**Sublevel** & **M** & **C** & **\(\sigma\)** & **min** & **max** & **R** & **Q1** & **Q3** & **IQR** & **S** & **K** \\ \hline Direct interaction & 17.83 & 13.08 & 13.82 & 2.09 & 59.13 & 57.04 & 9.39 & 24.81 & 15.43 & 1.47 & 1.84 \\ Indirect interaction & 7.83 & 6.19 & 6.20 & 0.66 & 40.66 & 40.00 & 4.42 & 9.64 & 5.22 & 3.29 & 15.13 \\ \hline \hline \end{tabular}
\end{table} 
Table 5: Statistical analysis of the time needed to complete tasks on sublevels of the third level. On the sublevel with horizontal orientation, the buttons were 0.24\(\times\)0.17 in size and arranged at a spatial distance of \(-\)10. The results show an average task time of 7.06 s with a standard deviation of 2.99 s. This shows that the participants became accustomed to the task relatively quickly. The median of 5.98 s and a relatively small IQR of 4.13 s indicate a constant performance of the participants in the task. In the vertical plane, the size of the button is reduced to 0.14\(\times\)0.13, and the spatial distance between the button and the virtual hand is increased to \(-\)15, resulting in a significantly higher mean processing time of 16.81 s. The large standard deviation of 13.09 s and a larger IQR of 13.88 s indicate fluctuations in the participants' performance, which points to difficulties in solving the task. This is a consequence of the increased task complexity caused by the smaller buttons and the larger spatial distance, requiring more precision from the participants. Although the distracting background sublevel uses the smallest buttons (0.12 \(\times\) 0.17), it places them closer to the participants (\(-\)5), possibly facilitating interaction. The average time to complete the task is similar to the first sublevel (7.24 s with a standard deviation of 3.39). The smaller IQR of 3.67 s indicates that the participants completed the task evenly despite the challenge posed by the smaller buttons. This means that the smaller distance can compensate for the smaller size of the buttons, allowing participants to interact with the buttons more successfully. In the sublevel with vertical orientation, higher values of the flatness index indicate the presence of several extreme values that reflect the challenges the participants faced.