## 7 Discussion  
As the previous section shows, the findings partially support our hypotheses. Regarding the UBT metrics, **H1** was supported as the participants in the RJAS Active condition showed significantly lower distraction frequency (\(f_{d}\)) than those in the Inactive condition, with a large effect size and high statistical power. This aligns with our expectation that the robot's RJA behavior would reduce the number of attentional disengagement events, helping the participants to remain more focused during the interaction. Similarly, **H2** was also supported: the distraction duration ratio (\(p_{d}\)) was significantly lower for the Active condition, again with a large effect and acceptable power. These results confirm that the RJAS not only reduced how often users looked away but also helped to shorten those disengagement episodes, reinforcing the system's effectiveness in sustaining user attention throughout the task (the game). Turning to self-reported engagement, **H3** was also supported, with significantly higher total UES-SF scores observed in the RJAS Active condition compared to the Inactive group. This result showed a medium-to-large effect size and moderate statistical power, supporting the practical relevance of the finding despite the limited sample size. This indicates that, as hypothesized, the participants perceived the interaction as more engaging when the robot responded to their attentional behavior. The dimension-specific exploratory hypotheses yielded more nuanced results. **H4** was supported as the participants reported significantly higher Focused Attention in the Active condition. This aligns with the expectation that the robot's attentional responsiveness would improve task immersion. However, **H\({}_{5}\)-H\({}_{7}\)** were not supported. Perceived Usability, Aesthetic Appeal, and Reward Factor did not differ significantly between the conditions, and the associated effect sizes and statistical power were negligible to low. These findings may indicate that attentional responsiveness, while effective in enhancing _Focused Attention_, may not be sufficient to influence broader engagement components such as _Perceived Usability_, _Aesthetic Appeal_, or _Reward Factor_. These aspects could depend more on the overall interaction flow--in this case, influenced by the game--the perceived expressiveness and appearance of the robot, or the user's expectations and prior experiences, which may have been relatively similar across the conditions. Nevertheless, the low statistical power observed for these dimensions suggests that future studies with larger sample sizes might reveal significant effects. These findings build upon previous work, where we demonstrated that RJA mechanisms increase the perceived social presence of the robot [20]. The current results go one step further, suggesting that this increased social presence may translate into higher perceived value of the interaction itself. In this case, the participants were not only more aware of the robot's social cues but also more invested in the shared task. The attentional responses of the robot may have enhanced the meaningfulness of the interaction, reinforcing the participant's engagement with the game and the robot as a collaborative partner. As a complementary step beyond our main hypotheses, we also performed exploratory correlational analyses to investigate potential relationships between self-reported and behavioral engagement metrics. Although neither of the objective engagement measures reached statistical significance in their correlation with the UES-SF Total Engagement score, both showed moderate negative associations in the expected direction. Specifically, higher self-reported engagement was associated with lower distraction frequency (\(r=-0.32\), \(p=0.068\)) and shorter distraction duration (\(r=-0.31\), \(p=0.085\)). The statistical power for detecting these effects was moderate (\(1-\beta=0.46\) and \(0.42\), respectively), which may have limited the ability to achieve significance.