## 5 Experiment Results and Discussion
### Comparison of Subjective Ratings of Interactions in SG1 and SG2  
To assess whether the method for determining the interaction mechanism settings is appropriate for the participants, we compared their ratings of interaction mechanisms from SG1 and SG2 (N = 107). A participant who did not rate at least one of the interaction \begin{table}
\begin{tabular}{c c c c} \hline  & **Translation** & **Scaling** & **Rotation** \\ \hline
**M** & 4.34 & 4.73 & 4.49 \\ \hline
**C** & 5 & 5 & 5 \\ \hline
**Sd** & 0.9 & 0.65 & 0.98 \\ \hline
**min** & 1 & 1 & 1 \\ \hline
**max** & 5 & 5 & 5 \\ \hline
**CI = 95\%** & 4.17; 4.51 & 4.61; 4.86 & 4.3; 4.68 \\ \hline \end{tabular} Note: M—mean, C—median, Sd—standard deviation, min—minimum, max—maximum, CI = 95%—95% confidence interval.  
\end{table} 
Table 11: Descriptive statistics for the subjective evaluation of interaction mechanisms in transformation tasks in SG2 (N = 108). Figure 16: Mean ratings of interaction mechanisms in transformation tasks in SG2 with 95% confidence intervals. mechanisms was excluded from the analysis. Assumptions behind the calculation of interaction mechanism for a particular task are that if a user skipped the task, then it is considered difficult for them, as well as that they gave the lower rating for such interaction mechanism. Also, it is considered that if a user rated one interaction mechanism of the related tasks with a higher rating, they prefer it more so that interaction mechanism is then assigned to them. In the end, if the ratings are the same for both interaction mechanisms of the related task, then it is considered that the more difficult interaction took them more time (and based on that they were assigned an alternative interaction in SG2). Based on these assumptions, the participant in SG2 should be more comfortable with the assigned interaction in a particular transformation task (compared to an alternative interaction), and the participant would give it a higher (or equal) rating compared to the average of the ratings given for interactions in equivalent tasks in SG1. The equation that describes the above written is:  
\[I_{2}\geq I_{1}\,\ I_{1}=\frac{\overline{I_{TG}+\overline{I_{IC}}}}{2} \tag{1}\]  
\(\overline{I_{TG}}\) and \(\overline{I_{IC}}\) are the mean ratings of the participants for different interaction mechanisms (TG = Touch Gestures and IC = Indirect Controls) for the same transformation task in SG1, I\({}_{1}\) are the mean values of the ratings I\({}_{\text{TG}}\) and I\({}_{\text{IC}}\) for one transformation task, and I\({}_{2}\) the mean score of interactions for the equivalent transformation task in SG2. The transformation task in SG1 refers to the tasks of translation (related tasks Translation TG-Translation IC), scaling (related tasks Scaling TG-Scaling IC), and rotation (related tasks Rotation TG-Rotation IC). By subtracting the mean values of the ratings I\({}_{1}\) from I\({}_{2}\) (I\({}_{2}\)-I\({}_{1}\)) we can compare the participants' ratings of interaction mechanisms in transformation tasks from SG1 and SG2. Figure 17 shows a chart with the results which shows a positive value for the Rotation and Scaling tasks. This indicates that the participants were, on average, more satisfied with the interaction mechanisms in these tasks in SG2 than with the interaction mechanisms in the equivalent tasks in SG1. A negative value for the translation task indicates that the participants were on average more satisfied with the interaction mechanisms in SG1 compared to the assigned interaction mechanism in SG2. To determine whether the obtained difference is statistically significant, the Wilcoxon signed-rank test was performed (N = 107). This test is appropriate since participants rated the interaction mechanisms for the same transformation tasks in both SG1 and SG2, creating paired ratings, which is suitable for this non-parametric test which does not require the assumption that the data follow a normal distribution.