## 3 Materials and Methods
### Fuzzy Inference
#### 3.2.7 Statistical Analysis  
Statistical Analysis on Engagement Index  
The following two comparisons were performed to determine whether there was a significant difference in terms of engagement index between game modes using the two EEG sensors:  
* Comparison 1 (Unicorn: tailored game mode versus non-tailored game mode). The difference in terms of engagement collected via a Unicorn sensor between the non-tailored game mode and the tailored game mode.
* Comparison 2 (Bitalino: tailored game mode versus non-tailored game mode). The difference in terms of engagement collected via a Bitalino sensor between the non-tailored game mode and the tailored game mode.  
First, Shapiro-Wilk tests were performed to determine whether the data followed a normal distribution. As a result of the Shapiro-Wilk tests, we performed a Wilcoxon-Signed-Rank test to determine whether there was a significant difference between the engagement index and the game modes in each EEG sensor used to collect the EEG data. We used an alpha = 0.05 for both statistical tests.  
Statistical Analysis on Participants' Opinions on Game Mode Preferences  
Regarding the participants' opinions on game mode preferences, we collected their opinions using questionnaires after finishing playing both game modes on the following: their favorite game mode, the easiest game mode to play (ease of play), the least frustrating game mode to play (frustration), the least boring game mode to play (boredom), the game mode with the fastest game response time to commands (game response time), and the most entertaining game mode (entertainment).  
We divided the questionnaires into two groups based on the sensor used to collect the EEG signal (i.e., experimental group 1--Bitalino sensor, and experimental group 2--Unicorn sensor). For each experimental group, the responses of each participant for each opinion (i.e., ease of play, frustration, boredom, game response time, and entertainment) and for each Likert scale value were added. As a result, there were frequency tables for ease of play, frustration, boredom, game response time, and entertainment per EEG sensor. Each frequency table showed the frequencies obtained in each Likert scale value. Additionally, a frequency table for each EEG sensor regarding the favorite mode was obtained. Specifically, these tables summarized the \"favorite mode\" frequencies reported for the non-tailored and the tailored modes in the experimental group 1 (Bitalino sensor) and experimental group 2 (Unicorn sensor). These tables were used to present the results and conduct the statistical analysis regarding the participants' opinions on game mode preferences.  
Table 1 presents the statistical tests performed to determine whether there was a significant association between the participants' opinion variables and the game modes; specifically, we performed chi-squared and [PERSON]'s exact tests to analyze this depending on the frequencies reported in each variable. It is important to note that a requirement for applying a chi-squared test is that the frequencies reported in each variable (i.e., in this case, the frequency reported in each Likert scale value) should be higher than five. [PERSON]'s exact test was applied in cases where a value of a Likert scale was lower than five. Furthermore, we considered only the Likert scale values that reported values higher than zero for both game modes. We used alpha = 0.05 for both statistical tests.