## 4 User Evaluation Method
### Stratification and Data Analysis  
To begin with, we point out that age distribution of males and females was quite different, and this could distort the results regarding between-subject comparisons. For example, if we were to find differences between genders, they might be due to the fact that males were on average younger than females, and not because of any real differences between genders. This is a common case of confounding variable: in fact, age behaves as a confounding variable in relation to the comparison between males and females. To control for confounding variables, we use stratification. Broadly speaking, stratification lets researchers control \"for confounding by creating two or more categories or subgroups in which the confounding variable either does not vary or does not vary very much\" [31].  
As stratification strategy, we divided participants in males and females and then in different age ranges. To identify age ranges, we looked for the best compromise to obtain (1) at least 10 participants for each gender, and (2) similar ages between the different genders. As shown in in Table 1, the mean age between males and females is nearly equivalent in any age groups (see mean difference column in Table 1), and this let us to control the effects of confounding variables. In fact, even assuming that age differences are statistically significant, practical importance is not relevant as reaction times increase at a rate of only \(\approx\)1 ms for each year of aging [14], and, in our case, the highest average age difference between males and females is only 2.5 years, corresponding to the age group 26-40. In this regard, please note that the concepts of statistical significance and practical importance (as referred in [32]) or substantive significance (as referred in [33]) are quite different.  
This study is both (1) within-subject, i.e., each participant has tried both \"Sound\" and \"Mute\" conditions to see if interfering auditory stimuli affect user performances  
\begin{table}
\begin{tabular}{l l l l l l} \hline \hline
**Age Group** & **Gender** & **Participants** & **Mean Age** & **SD** & **Mean Difference** \\ \hline \multirow{2}{*}{18–25} & M & 26 & 22.8 & 1.7 & \multirow{2}{*}{1.3} \\ \cline{2-5}  & F & 17 & 21.5 & 2.2 & \\ \hline \multirow{2}{*}{26–40} & M & 12 & 30.0 & 4.7 & \multirow{2}{*}{2.5} \\ \cline{2-5}  & F & 16 & 32.5 & 4.2 & \\ \hline \multirow{2}{*}{41+} & M & 11 & 53.5 & 9.6 & \multirow{2}{*}{1} \\ \cline{2-5}  & F & 18 & 54.5 & 9.4 & \\ \hline \hline \end{tabular}
\end{table}
Table 1: Stratification of participants in age ranges and genders with standard deviation (SD) and absolute difference between means.  
(first research question), and (2) between-subject, i.e., different ages and genders were compared to see if there are differences in terms of performances (second research question). For both within-subject and between-subject comparisons, we used nonparametric tests to detect significant differences since some data were not normally distributed (according to Shapiro-Wilk test). Particularly, when comparing \"Sound\" and \"Mute\" conditions, we used the (paired) Wilcoxon Signed-Rank test to detect significant differences in terms of (1) activation times, (2) error rates, and (3) perceived ease of synchronization. Regarding genders, we performed the (unpaired) Wilcoxon Rank Sum test to see any significant differences between males and females in the different age ranges. Moreover, in regards to age, we used the Spearman's rank-order correlation to assess the relation between (1) age and times of activation, and (2) age and error rate for both males and females separately. We also highlight that to identify any differences between different ages, males and females are treated separately to avoid gender acting as a confounding variable. Finally, results are presented using the median (instead of the mean) to avoid skewing possibly caused by non-normality.