# Combining Virtual Reality and Organizational Neuroscience for Leadership Assessment
## 3 Materials and Methods
### Statistical Analysis  
One person did not complete the questionnaire, and hence, answers from the remaining 55 subjects were analyzed. A multivariate outlier analysis [37] was performed to detect and remove any participant whose leadership score could be considered as extreme. For this purpose, the Mahalanobis distance between participants was calculated using their self-reported ROL and TOL scores. Then, the probability of this distance belonging to a Chi-square distribution was calculated. If this probability was below 0.01, the participant's scores were defined as outliers, whereupon the participant was excluded from further analysis. After such an analysis, four participants were removed resulting in a final sample size of 51.  
Both leadership subscales were categorized into high or low scores based on the mean of each variable, as they were normally distributed (\(p>0.05\), Shapiro-Wilk test). This was a necessary step for building the Machine Learning (ML) models, described in the following section. This categorization was then used in describing the variables and calculating the mean and standard deviation of low and high scores in each group. Furthermore, contrasts of hypotheses were performed to find any statistically significant difference that could be related to leadership scores. Using the categorization of the leadership scores to define two groups, different statistical tests were applied to the variables from the RV, depending on their nature (numerical/categorical) and normality (\(p\)-value of Shapiro-Wilk test). As a first explorative description of ROL and TOL, statistical tests were performed considering both high and low levels. If the variable was categorical, a Chi-square test was performed. If the variable was numerical, either t-test or Wilcoxon test was performed, according to its Gaussianity. Statistical significance level was set as alpha \(<0.05\).  
\begin{table}
\begin{tabular}{c c c} \hline \hline
**Group of Variables** & **Definition** & **Number of Variables** \\ \hline Situations & Decision-making & 29 \\ \hline \multirow{8}{*}{Eye Tracking} & Role of the virtual & Mean time (s) & 9 \\  & agent the & Mean number of \\  & participant was & fixations (n) & 9 \\  & looking at & Mean fixation time (s) & 9 \\  & in that moment & Mean time to first \\  & fixation (s) & 9 \\ \cline{2-3}  & Virtual agent the & Mean time (s) & 5 \\  & participant & Mean number of \\  & was looking at & fixations (n) & 5 \\  & & Mean fixation time (s) & 5 \\  & & Mean time to first \\  & & fixation (s) & 5 \\ \hline \hline \end{tabular}
\end{table}
Table 1: Description of the variables extracted from the decisions made and the behavior of the participant in terms of eye movement during the serious game.  
\begin{table}
\begin{tabular}{c c} \hline \hline
**Metric** & **Definition** \\ \hline Mean time (s) & Mean time the participant looked at the defined virtual agent/role during the whole experience. \\ Mean number of fixations (s) & Mean number of times the participant fixed the sight on the particular virtual agent/role during the whole experience. \\ Mean fixation time (s) & Mean time that each fixation in a virtual agent/role lasted during the whole experience. \\  & Time to first fixation is the time that elapses from the beginning of the experiment until the first time the eyes are fixed on the virtual agent/role. This metric defines the mean time to first fixation after the whole experience. \\ \hline \hline \end{tabular}
\end{table}
Table 2: Eye-tracking metrics extracted during the serious game.