## 4 Results
### Flow State Construct: J48 Decision Tree and Logistic Regression Analysis  
#### 4.2.1 J48 Decision Tree  
To answer RQ2, Weka's classifiers.trees.J48 was used to data-mine the relationship between variables. As the results of chi-square analyses indicated that ST-tp was not significant, only item difficulty, LT-tp, self-efficacy, and cognitive load were input into the classifiers with the outcome variable (EEG-F). The classifier mode for EEG-F (high vs. low EEG-F) was presented, and the cognitive load serves as the parent node (Node 1), as shown in Figure 2. \begin{table}
\begin{tabular}{c c c c c} \hline \hline \multirow{2}{*}{
\begin{tabular}{c} **Predictor** \\ **Variables** \\ \end{tabular} } & \multirow{2}{*}{**Groups**} & \multicolumn{2}{c}{**EEG-F**} & \multirow{2}{*}{**Total**} \\ \cline{3-3} \cline{5-5}  & & **Low EEG-F 1** & & \\ \hline \multirow{2}{*}{Self-efficacy} & Low self-efficacy & 326 (42.6\%) *** & 164 (21.4\%) & 490 (64.0\%) \\  & High self-efficacy & 97 (12.7\%) & 179 (23.4\%) *** & 276 (36.0\%) \\ \hline \multirow{2}{*}{LT-tp} & Low LT-tp & 223 (29.1\%) *** & 126 (16.4\%) & 349 (45.6\%) \\  & High LT-tp & 200 (26.1\%) & 217 (28.3\%) *** & 417 (54.4\%) \\ \hline \multirow{2}{*}{ST-tp} & Incorrect & 42 (5.5\%) & 25 (3.3\%) & 67 (8.7\%) \\  & Correct & 381 (49.7\%) & 318 (41.5\%) & 699 (91.3\%) \\ \hline \multirow{2}{*}{Difficulty} & Low difficulty & 247 (32.2\%) & 240 (31.3\%) *** & 487 (63.6\%) \\  & High difficulty & 176 (23.0\%) *** & 103 (13.4\%) & 279 (36.4\%) \\ \hline \multicolumn{2}{c}{Total} & \multicolumn{2}{c}{423 (55.2\%)} & 343 (44.8\%) & 766 (100\%) \\ \hline \hline \end{tabular} Note. * \(p<0.05\), ** \(p<0.01\), *** \(p<0.001\); dependent variable = high EEG-F vs. low EEG-F; LT-tp: long-term test performance; H: high; L: low; OR: odds ratio. 1 A low EEG-F means that the student is in a low flow state, as detected by an EEG. 2 A high EEG-F means that the student is in a high flow state, as detected by an EEG. 2  
\end{table} 
Table 1: _Cont._  
Figure 2: J48 decision tree for electroencephalogram (EEG)–detected, real-time flow state (EEG-F) factors. In Node 1, the sample is divided into high (Node 2) and low cognitive load (Node 3), which then classified the sample according to the levels of self-efficacy: high and low self-efficacy. In particular, Leaf 1 showed that when this student had a high cognitive load and low self-efficacy, a low EEG-F was induced (total instances: 167.0; incorrect instances: 10.0). In contrast, Leaf 2 showed that a high EEG-F emerged when the student had a low cognitive load and high self-efficacy (176.0/40.0). These relationships demonstrated that the interaction between the participant's cognitive load and self-efficacy influenced her flow experience. For Node 4 (high cognitive load and high self-efficacy) and Node 5 (low cognitive load and low self-efficacy), the sample was divided into high and low LT-tp. In particular, Leaf 3 showed that a student with a high cognitive load, high self-efficacy, and low LT-tp induced a low EEG-F (40.0/7.0). Similarly, Leaf 4 showed that a student with a low cognitive load, low self-efficacy, and high LT-tp had a low EEG-F (136.0/56.0). Ultimately, these findings showed that the effect of a student's LT-tp on flow experiences might vary. Ultimately, for Node 6 (high cognitive load and high self-efficacy with high LT-tp) and Node 7 (low cognitive load and low self-efficacy with low LT-tp), the sample was divided into high and low difficulty. Leaf 5 showed that when the student had a high cognitive load and high self-efficacy with high LT-tp for low difficulty, she had a high EEG-F (40.0/12.0). In contrast, Leaf 6 showed that when she had a high cognitive load and high self-efficacy with high LT-tp for high difficulty, she had a low EEG-F (20.0/8.0).