## 6 Results
### Quantitative Results
#### 6.1.3. Correlational Analysis  
Although not directly hypothesized, in order to assess whether self-reported engagement aligns with observable behavior, we conducted exploratory correlational analyses to examine the relationship between the self-reported and behavioral engagement metrics. We  
\begin{table}
\begin{tabular}{l l l l l l l l} \hline \hline
**Measure** & **Dimension** & **Condition** & **N** & **Average** & **SD** & \(p\) & **Power** \\ \hline \multirow{4}{*}{UBT} & \multirow{4}{*}{\(f_{d}\)} & Active & 16 & 0.0091 & 0.0044 & **0.002** & **0.94** \\  & & Inactive & 20 & 0.0226 & 0.0161 & & \\ \cline{2-8}  & & \multirow{2}{*}{\(\rho_{d}\)} & Active & 18 & 0.0554 & 0.0252 & **0.026** & **0.76** \\  & & Inactive & 18 & 0.1015 & 0.0774 & & \\ \hline \multirow{4}{*}{UES-SF} & Total Engagement & Active & 19 & 4.16 & 0.39 & **0.043** & **0.66** \\  & & Inactive & 18 & 3.93 & 0.28 & & \\ \cline{2-8}  & \multirow{2}{*}{Focused Attention} & Active & 19 & 3.89 & 0.63 & **0.028** & **0.73** \\  & & Inactive & 18 & 3.44 & 0.56 & & \\ \cline{2-8}  & \multirow{2}{*}{Perceived Usability} & Active & 19 & 4.37 & 0.53 & 0.842 & 0.07 \\  & & Inactive & 19 & 4.33 & 0.54 & & \\ \cline{2-8}  & \multirow{2}{*}{Aesthetic Appeal} & Active & 20 & 3.85 & 0.71 & 0.950 & 0.06 \\  & & Inactive & 20 & 3.87 & 0.94 & & \\ \cline{2-8}  & \multirow{2}{*}{Reward Factor} & Active & 20 & 4.43 & 0.66 & 0.789 & 0.07 \\  & & Inactive & 16 & 4.63 & 0.27 & & \\ \hline \hline \end{tabular}
\end{table}
Table 3: Summary of results across engagement measures, dimensions, and experimental conditions. Statistically significant values (\(p<0.05\)) and powers above 0.65 are shown in bold.  
Figure 7: Bar charts with the average scores and SDs of each user engagement dimension measured by the UES-SF. Significance level is indicated as \({}^{*}\) for \(p<0.05\).  
believe this analysis might offer a more comprehensive understanding of user experience, in addition to revealing unexpected relationships worth testing in confirmatory studies in the future.  
A Pearson correlation was conducted to examine the relationship between participants' self-reported engagement (UES-SF Total Engagement score) and the distraction frequency measured by the UBT system. The analysis revealed a moderate negative correlation (\(r=-0.32\), \(p=0.068\), \(n=33\)), suggesting that higher reported engagement tended to be associated with fewer observed distractions, although the result did not reach significance. The statistical power for detecting this effect was moderate (\(1-\beta=0.46\)).  
With respect to the relationship between participants' self-reported engagement (UES-SF Total Engagement score) and the distraction duration ratio, the analysis also revealed a moderate negative correlation (\(r=-0.31\), \(p=0.085\), \(n=33\)), indicating that higher engagement scores tended to be associated with less time spent distracted. However, this correlation also did not reach statistical significance. The power for this test was similarly moderate (\(1-\beta=0.42\)).  
We additionally explored whether any specific UES-SF dimensions were associated with distraction metrics. Among them, _Focused Attention_ exhibited a negative correlation with distraction frequency (\(r=-0.25\), \(p=0.158\), \(n=33\)), suggesting that those participants who felt more absorbed tended to exhibit fewer observable distractions, although this trend was not statistically significant and the power to detect this effect was limited (\(1-\beta=0.30\)). No correlations were found between the remaining UES-SF dimensions and the objective engagement metrics, indicating that alignment between self-reported and behavioral data may be strongest for attentional aspects of engagement.