## 5 Data Collection and Analysis  
### Physiological Cognitive Workload Using Pupil Diameter  
Given that the participants experienced four primary interruption task sets with each of the three interruption modes, a total of 480 pupil diameters (40 participants with 12 task scenarios) averaged for both eyes in each task scenario were obtained. To achieve a uniform sampling rate of 120 Hz, a one-dimensional data interpolation method was employed for the raw measurements. From the collected data, we excluded 11 data that were noisy or failed to detect pupil diameter accurately, and the total number of calculated averages was 469 cases. Though the loss of data did not distort our counterbalanced design, a single imputation method was used to fill in the missing data [58]. Means and standard deviations for pupil diameters for all participants can be found in Table 3 and Figure 4.  
We conducted a 4 (task set) \(\times\) 3 (interruption mode) repeated-measures ANOVA to examine the separate and combined influences of these factors on pupil diameter. [PERSON]'s test checked if the sphericity assumption was violated in our pupil data for the effect of task set (\(\chi^{2}\) (5) = 2.412, \(p\) = 0.061) and the effect of interruption mode (\(\chi^{2}\) (2) = 10.162, \(p\) < 0.001), and the interaction between task set and interruption mode (\(\chi^{2}\) (27) = 47.262, \(p\) < 0.001). Therefore, Greenhouse-Geisser corrections are reported here. We observed a significant main effect of task set on pupil diameter (F (3.921, 48.421) = 47.143, \(p\) < 0.05). Post hoc least significant difference (LSD) comparisons revealed significant differences in pupil diameter among task sets, except for the comparisons between the skill/cognitive set and skill/skill set (\(p\) > 0.05). Participants' pupil diameters were more dilated in cognitive primary task sets (cognitive/cognitive and cognitive/skill sets) than skill primary task sets (skill/cognitive and skill/skill sets) in all three interruption modes. However, there was no difference in the cognitive/cognitive and cognitive/skill sets in the negotiated mode. This omnibus test also revealed a significant main effect of interruption mode on pupil diameter (F (1.368, 25.990) = 71.903, \(p\) < 0.05). Post hoc LSD comparisons showed that pupil diameters decreased with the order of the immediate, the scheduled, and the negotiated modes. Another result observed within this omnibus test was that there was no significant interaction between interruption mode and task set on pupil diameter (F (4.356, 82.767) = 3.633, \(p\) > 0.05).  
\begin{table}
\begin{tabular}{c c c c} \hline \multicolumn{2}{c}{**Pupil Diameter**} & \multicolumn{2}{c}{**Mean**} & \multicolumn{2}{c}{**Standard Deviation**} \\ \hline \multicolumn{2}{c}{**(Average Value for Both Eyes)**} & \multicolumn{1}{c}{**(mm)**} & \multicolumn{1}{c}{**(mm)**} \\ \hline \multirow{3}{*}{Cognitive/cognitive task set} & Immediate & 4.553 & 0.573 \\  & Scheduled & 4.199 & 0.474 \\  & Negotiated & 3.520 & 0.529 \\ \hline \multirow{3}{*}{Cognitive/skill task set} & Immediate & 4.035 & 0.538 \\  & Scheduled & 3.967 & 0.443 \\  & Negotiated & 3.479 & 0.394 \\ \hline \multirow{3}{*}{Skill/cognitive task set} & Immediate & 3.700 & 0.388 \\  & Scheduled & 3.572 & 0.327 \\  & Negotiated & 3.001 & 0.327 \\ \hline \multirow{3}{*}{Skill/skill task set} & Immediate & 3.646 & 0.362 \\  & Scheduled & 3.462 & 0.273 \\ \cline{1-1}  & Negotiated & 3.013 & 0.255 \\ \hline \end{tabular}
\end{table}
Table 3: Descriptive statistics of pupil diameters under each task set.