## 2 Methods
### Data Processing and Statistical Analysis
#### 2.4.2 Gaze Entropy  
A gaze plot and a heat map that express the overall movement of the gaze can be utilized in gaze movement analysis. Gaze plots and heat maps effectively analyze the overall pattern of gaze movement, but they have the disadvantage of being difficult to measure quantitatively [16]. In order to solve this problem, a method for calculating entropy from a gaze plot and a heat map using the concept of information theory has been studied. Entropy in information theory is the average information or uncertainty associated with a choice [17]. This concept of entropy has been adopted to measure system complexity [18; 19]. In this context, entropy has been used since the early 1980s to analyze the complexity of gaze movement. Nevertheless, it is only recently that the concept of gaze entropy has been used in earnest [20]. There are few cases of studying the characteristics of gaze entropy in SA. [PERSON] et al. [3] studied whether gaze tracking could be a means to determine SA in flight situations and confirmed that pilots' gaze entropy increased when SA was low. [PERSON] et al. [21] studied a method to quantitatively measure SA using gaze entropy during an abnormal situation in a chemical power plant. They found a significant difference in gaze entropy between the group that succeeded and the group that did not succeed in the task. From the above studies, it was found that gaze entropy tends to decrease when SA is high. Methods for using entropy for gaze movement analysis can be primarily divided into two: using a gaze plot and using a heat map [18]. The entropy types derived from the gaze plot are Shannon entropy, dwell time entropy, and Markov entropy. The value derived from the heat map is called heat map entropy. This study used Shannon entropy, Markov entropy, dwell time entropy, and heatmap entropy to analyze a participant's gaze movement. The four gaze entropy measures have complementary characteristics in eye movement analysis, but there was no case in which all four entropy measures were used to analyze SA and gaze movement. In this study, all four gaze entropies were used to analyze the gaze movements of women and men in SA. The concept and calculation method of the four gaze entropies are as follows. Shannon entropy is the method that utilizes the number of times the eye stays in the Area Of Interest (AOI) [20; 22]. Five AOIs, which are indicators that provide information necessary to determine the four accident situations, Rx Power, RV water level, PZR Pr., CTMT Rad., and CTMT Pressure, were defined. Shannon entropy is defined as follows [20; 22]:  
\[H=-\sum_{i=1}^{n}P_{i}\log_{2}P_{i} \tag{1}\]  
In this equation, \(P_{i}\) is the ratio of the relative fixation count divided by the fixation count of the \(i\)th AOI by the total fixation count of all AOIs, and \(n\) is the number of all AOIs. Therefore, if the value of Shannon entropy obtained from the gaze plot is high, the user's gaze is distracted; if it is low, it means that the user's gaze is focused on specific AOIs. However, Shannon entropy does not take into account the eye movement pattern between AOIs. Markov entropy is determined using a Markov chain model, a stochastic model describing a sequence of possible events where the probability of each event depends only on the state attained in the previous event. Markov entropy is obtained using the state space at a specific point in time and a transition matrix representing the probability of transition between states. Markov entropy is calculated using the time the eye stays on the AOIs and the transition probability between the AOIs [17; 23]. It is defined as follows [20; 23]:\[H=-\sum_{i=1}^{n}P_{i}\sum_{j\
eq 1}P_{ij}\log_{2}P_{ij} \tag{2}\]  
Here, the state set is defined as the set of initial probabilities of each AOI, and the transition matrix is defined as a matrix of transition probabilities between AOIs. The initial probability \(P_{i}\) of the \(i\)th AOI is a value obtained by dividing the fixation count of the ith AOI by the total fixation count of all AOIs.