## 4 Results
### Survival Analysis  
To further investigate the effects of different conditions on turn-timing, we applied survival analysis to evaluate the time delay between the expression of speaking intentions and the actual speech initiation. By comparing survival curves across different clusters, we aim to reveal behavioral differences in turn-timing choices under varying scenarios.  
Specifically, for all successful speaking intention tags (including both non-overlapping and overlapping cases), the time of intention expression was set as the starting point for survival analysis, while the actual speech initiation was defined as the \"event\". By measuring the time interval between the tag and the event, we calculated the \"survival rate\" of intentions at each time point. Figure 7 presents the survival curves for each category, providing a visual representation of the dynamics of speaking intention realization across different scenarios.  
The log-rank test results indicate that the difference between C1 and C4 scenarios is statistically significant (\(p<0.01\)). Through the analysis of the survival curves, it can be observed that in C4, the likelihood of speaking intentions being converted into actual speech shortly after expression is significantly lower than in other categories (i.e., the survival probability is higher). This suggests that in C4 (low-activity Scenario), participants are more inclined to delay the execution of their speaking intentions rather than speak immediately. In contrast, in C1, the survival probability drops to the lowest among all categories after 1 s, suggesting that speaking behaviors in C1 (prolonged single-turn scenario) are less likely to be delayed for a longer period.  
Further analysis of survival probability after 1.5 s reveals that these probabilities in C1 and C5 are significantly lower compared to C2, C3, and C4. This suggests that in C1 (prolonged single-turn scenario) and C5 (high-competition scenario), speaking intentions  
\begin{table}
\begin{tabular}{l c c c c} \hline \hline
**Cluster** & **Instances** & **Conflicting** & **Unsuccessful** & **Obstructed** \\  & **(Count)** & **(Ratio)** & **(Ratio)** & **(Ratio)** \\ \hline Prolonged Single-turn Scenario (C1) & 154 & 29.9\% & 18.8\% & 48.7\% \\ High-status Role Scenario (C2) & 96 & 27.1\% & 8.3\% & 35.4\% \\ Intense Interaction Scenario (C3) & 36 & 38.9\% & 13.9\% & 52.8\% \\ Low-activity Scenario (C4) & 136 & 5.2\% & 11.8\% & 17.0\% \\ High-competition Scenario (C5) & 69 & 40.6\% & 27.5\% & 68.1\% \\ \hline \hline \end{tabular}
\end{table}
Table 4: Speaking intention outcomes across clusters (conflicting cases and unsuccessful cases combine to form obstructed cases).  
Figure 7: The Kaplan-Meier survival curves for each cluster, where the survival state indicates that speaking intentions have not yet been converted into actual speaking behavior.  
that successfully transition into actions are mostly concentrated within 1.5 s after the intention is expressed. Speaking intentions that are not acted upon within 1.5 s are relatively rare, indicating that they are often abandoned and become unsuccessful intentions. In contrast, in C2 (high-status role scenario), C3 (intense interaction scenario), and C4 (low-activity scenario), approximately 20% of speaking intentions remain unfulfilled even after 1.5 s. This difference may reflect variations in participants' patience or strategies for acquiring speaking turns across different scenarios, highlighting the influence of contextual factors on speaking intention outcomes.