## 6 Results
### Quantitative Results
#### 6.1.2 Self-Reported Measure (UES-SF)  
After analyzing the objective results, this section describes the results obtained from the UES-SF questionnaire, which served as the self-reported measure of user engagement. The UES-SF evaluates participants' perceived engagement through four dimensions (_Focused Attention_, _Perceived Usability_, _Aesthetic Appeal_, and _Reward Factor_) as well as a _Total Engagement_ score. These metrics provide insight into the participants' internal experiences during the interaction with the robot, complementing the behavioral perspective captured by the UBT system. Concerning _Total Engagement_, one participant from the RJAS Inactive condition and two from the Active condition exceeded the bounds for overall engagement. As a result, the final sample included 18 participants in the Inactive condition and 19 in the Active condition. Shapiro-Wilk tests confirmed that the overall engagement scores were normally distributed in both the Inactive (\(W=0.939\), \(p=0.275\)) and Active (\(W=0.952\), \(p=0.428\)) conditions. The subsequent independent-samples \(t\)-test revealed that the participants in the RJAS Active condition (\(M=4.16\), \(SD=0.39\)) reported significantly higher overall engagement scores than those in the Inactive condition (\(M=3.93\), \(SD=0.28\)), \(t(35)=2.102\), \(p=0.043\). The resulting Cohen's \(d\) reflects a medium-to-large effect size (\(d=0.69\)), and the sample shows moderate statistical power to detect the effect (\(1-\beta=0.66\)). Figure 6 shows the results for the UES-SF Total Engagement. Figure 5: Bar chart with the average scores and SDs for each UBT metric. Significance levels are indicated as * for \(p<0.05\) and ** for \(p<0.01\). After analyzing the overall engagement score, we proceeded to examine each UES-SF dimension separately. These results were examined to better understand the nature of the overall engagement effect and were not subjected to confirmatory hypothesis testing. Therefore, no correction for multiple comparisons was applied to the \(p\)-values associated with these exploratory tests. For _Focused Attention_, outliers were identified, resulting in the exclusion of one participant from the RJAS Active condition and two from the Inactive condition. The final sample thus included 19 and 18 participants, respectively. This dimension also passed normality tests in both conditions (Inactive: \(W=0.960\), \(p=0.604\); Active: \(W=0.917\), \(p=0.099\)). Group means revealed higher _Focused Attention_ scores in the RJAS Active condition (\(M=3.89\), \(SD=0.63\)) compared to the Inactive condition (\(M=3.44\), \(SD=0.56\)). An independent-samples \(t\)-test confirmed that this difference was statistically significant, \(t(35)=2.30\), \(p=0.028\), with a mean difference of 0.45. The effect size was medium-to-large (\(d=0.75\)), with a statistical power of 0.73 to detect this effect. For _Perceived Usability_, one outlier was excluded from each group, resulting in 19 participants per condition. The normality assumption was slightly violated in the Active condition (\(W=0.896\), \(p=0.041\)), while it held in the Inactive condition (\(W=0.907\), \(p=0.066\)). However, visual inspection of the distribution and the robustness of the \(t\)-test justified proceeding with a parametric comparison. The participants in the Active condition reported slightly higher usability scores (\(M=4.37\), \(SD=0.53\)) than those in the Inactive condition (\(M=4.33\), \(SD=0.54\)), but this difference was not statistically significant (\(p=0.842\)). The effect size was negligible (\(d=0.07\)), and the statistical power to detect such an effect was very low (\(1-\beta=0.07\)). Regarding _Aesthetic Appeal_, no outliers were identified and all the participants were retained in the analysis (\(n=20\) per condition). Normality was confirmed in both groups (Inactive: \(W=0.918\), \(p=0.090\); Active: \(W=0.929\), \(p=0.151\)), and variances were assumed equal.