## 6 Results
### Quantitative Results
#### 6.1.1 User Behavioral Measures (UBT)  
This subsection presents the results obtained from the UBT system, which served as the objective assessment of user engagement. Based on head pose telemetry data, we computed two key indicators of attentional disengagement: distraction frequency (\(f_{d}\)) and distraction duration ratio (\(\rho_{d}\)). These metrics are designed to reflect how often and for how long the participants looked away from the robot, offering a behavioral perspective on the impact of the RJAS on user attention during the interaction.  
First, regarding the distraction frequency (\(f_{d}\)), outliers were identified using boxplot analysis with a \(1.5\times IQR\) (interquartile range) rule. Specifically, any data point lying more than \(1.5\times IQR\) above the third quartile or below the first quartile was considered an outlier and removed from the analysis. This method, known as Tukey's rule, is widely used for ensuring that the measures are not skewed by anomalously high or low data points. Four participants in the Active condition exceeded the upper bound for \(f_{d}\) and were excluded from the analysis. As a result, the final sample included 16 participants in the Active condition and 20 in the Inactive condition. Shapiro-Wilk tests confirmed that distraction frequency was normally distributed in both the Inactive (\(W=0.933\), \(p=0.179\)) and Active (\(W=0.937\), \(p=0.318\)) conditions.  
Next, an independent-samples \(t\)-test revealed that the participants in the RJAS Active condition (\(M=0.0091\), \(SD=0.0044\)) exhibited significantly lower distraction frequency than those in the Inactive condition (\(M=0.0226\), \(SD=0.0161\)), \(t(22.52)=-3.564\), \(p=0.002\). The mean difference was \(-0.0134\), with a large effect size (\(d=1.08\)) and high statistical power (\(1-\beta=0.94\)) to detect this effect.  
Looking at the distraction duration ratio (\(\rho_{d}\)), we also observe some outliers from the original 20-20 group. Two participants from each condition were excluded as a result of the boxplot analysis. As a result, the final sample included 18 participants in the Inactive condition and 18 in the Active condition. The Shapiro-Wilk tests revealed that the distraction duration ratio was normally distributed in the Active condition (\(W=0.948\), \(p=0.393\)) but not in the Inactive condition (\(W=0.888\), \(p=0.036\)). Although the normality test indicated a significant deviation from normality in the Inactive condition, the Kolmogorov-Smirnov result was non-significant (\(p=0.054\)), and visual inspection of the histogram revealed no severe normality infractions. The distribution was slightly right-skewed but showed no extreme values or multimodality. Given the approximatesymmetry and the robustness of the \(t\)-test under soft normality infractions, particularly with balanced group sizes, we proceeded with the parametric analysis.  
In this case, the \(t\)-test revealed that the participants in the RJAS Active condition (\(M=0.0554\), \(SD=0.0252\)) exhibited significantly lower \(\rho_{d}\) than those in the Inactive condition (\(M=0.1015\), \(SD=0.0774\)), \(t(20.56)=-2.405\), \(p=0.026\). The mean difference was \(-0.0461\), showing a large effect size (\(d=0.80\)) and acceptable statistical power (\(1-\beta=0.76\)) to detect this effect. All the results for both UBT metrics are shown in Figure 5.