## 3 Methodology
### Analysis Methods
#### 4.1.1 Alarm-Set Usage  
**Set Frequency. ** There are three variables in the set frequency, _freq_use_days_, _prop_use_days_, and _avg_daily_alarm_. First, the number of days of setting each wake-up task (_freq_use_days_) was compared via the Kruskal-Wallis \(H\) test, The results show significant and moderate differences among the wake-up tasks [\(H(3)=10,884.67\), \(p<0.001\), \(e^{2}=0.036\)]. Post-hoc comparisons using the Dunn test also found significant differences in most of the pairs of the wake-up tasks, but their magnitudes of the difference differed depending on the task pair. _Normal_task_ was used 54 days on average, and this is much greater than those of others (vs. _picture_task_: \(d=0.491\), vs. _shake_task_: \(d=0.471\), vs. _math_task_: \(d=0.252\)). _math_task_ tended to have a moderately lower number of days than _picture_task_ (\(d=0.251\)) and _math_task_ (\(d=0.226\)). However, the difference in the frequencies of _picture_task_ uses and _shake_task_ uses was not significant and not considerable (\(p=0.278\), \(d=0.023\)). Next, there is a significant and moderate difference in the proportion of setting each wake-up task (_prop_use_days_) [\(H(3)=15,704.64\), \(p<0.001\), \(e^{2}=0.052\)], and all the post-test results are also statistically significant. The effect sizes of the post-tests show the detailed relationship between the wake-up tasks. The proportion of days with _normal_task_ is much greater than those of others (vs. _picture_task_: \(d=0.553\), vs. _shake_task_: \(d=0.585\), vs. _math_task_: \(d=0.337\)). _shake_task_ and _picture_task_ showed a similar number of uses (\(d=0.032\)), and _math_task_ was the least used (vs. _shake_task_: \(d=0.254\) and vs. _picture_task_: \(d=0.222\)). We also found a significant and moderate difference in the number of set alarms in a day (_avg_daily_alarm_, multiple alarm-sets in a day) [\(H(3)=13,852.05\), \(p<0.001\), \(e^{2}=0.046\)]. What all tasks had in common was that users tended to set a single alarm for a day (_normal_task_: 1.55, _picture_task_: 1.16, _shake_task_: 1.34, _math_task_: 1.36). However, the effect sizes showed a large difference between particular task pairs. For example, the number of _normal_task_ alarms tended to be greater than those of the other tasks, and its effect size also showed that the magnitude of their differences was considerably large (vs. _picture_task_: \(d=0.624\), vs. _shake_task_: \(d=0.351\), \begin{table}
\begin{tabular}{c c c c c c c} \hline \hline \multirow{2}{*}{**Variable**} & \multicolumn{4}{c}{**Wake-Up Task: Mean (SD)**} & \multirow{2}{*}{\(H\)} & \multirow{2}{*}{\(p\)**-Value**} & \multirow{2}{*}{\(\boldsymbol{e^{2}}\)} \\ \cline{2-2} \cline{5-6}  & **Normal** & & & & & \\ \hline
**Dismiss Time** & & & & & \\
**Duration** & **14.10** & **40.06** & **26.62** & **40.81** & & \\ _avg_task_completion_time_ & (7.18) & (15.09) & (12.34) & (15.49) & 144,454.19 & \(<\)0.001 & **0.683** \\ _sd_task_completion_time_ & **11.86** & **15.63** & **12.89** & **14.67** & & \\  & (6.22) & (8.01) & (6.39) & (5.61) & 14,281.84 & \(<\)0.001 & **0.067** \\ \hline
**Snooze** & & & & & & \\ _avg_freq_snooze_ & **0.16** & **0.33** & **0.20** & **0.19** & & \\  & (0.25) & (0.51) & (0.32) & (0.33) & 277.76 & \(<\)0.001 & 0.001 \\ _sd_freq_snooze_ & **0.27** & **0.30** & **0.28** & **0.28** & & \\  & (0.27) & (0.31) & (0.30) & (0.28) & 16.18 & \(<\)0.001 & 0.001 \\ \hline \hline \end{tabular}
\end{table} 
Table 3: Alarm dismiss-usage comparison among the wake-up tasks (Kruskal–Wallis H test). Figure 3: The magnitude of task-wise mean differences on alarm dismiss-usage: [PERSON]’s \(d\) (col, row). vs. _math_task_: \(d=0.314\)). Similarly to the _prop_use_days_, the effect size of the difference between _shake_task_ and _math_task_ was relatively small (\(d=0.047\)), and they were frequently used in a day more than _picture_task_ (vs. _shake_task_: \(d=0.391\) and vs. _math_task_: \(d=0.425\)). **Set Time. ** The set time category includes _avg_ring_hour_ and _prop_weekday_.