## 4.
### Data Analysis and Statistical Methods
#### 3.5.1 Descriptive Statistics and Data Normalization
Paired \(t\)-tests revealed significant improvements in conceptual mastery for both groups: the experimental group (AI-driven feedback) demonstrated a highly significant increase (\(t\)(349) = 14.72, \(p<0.001\)), while the control group (instructor-led feedback) also showed a significant but less pronounced improvement (\(t\)(349) = 2.53, \(p=0.012\)). These results underscore the superior efficacy of AI-driven adaptive feedback over traditional methods. To assess engagement levels, we analyzed interaction frequency with the AI system. The number of feedback interactions per week was compared between students who improved the most and those who showed minimal progress as shown in Table 8.  
The \"engagement increase\" represents the percentage improvement in student interaction frequency with the AI-driven feedback system (experimental group) or traditional feedback (control group) over the 20-week period. It was calculated by comparing the baseline engagement--average weekly interactions in Week 1 (e.g., 13.5 for high performers in the experimental group)--to the overall study average (e.g., 18.2), yielding a 35% increase for high performers. Interactions were tracked via system logs, capturing actions such as accessing feedback, completing adaptive tasks, or responding to AI prompts. This metric reflects how consistently students engaged with the feedback mechanisms, correlating higher engagement with greater performance gains, as validated by the regression analysis (\(R^{2}\) = 0.76, \(p<0.001\)). In this study, \"engagement\" is defined as the extent of active student participation with the feedback system, encompassing actions such as logging into the AI platform, reviewing feedback, completing adaptive tasks, and interacting with AI-generated prompts or instructor comments. It was measured through system-generated logs that recorded these interactions at five-minute intervals, capturing metrics like frequency (e.g., average weekly interactions), duration (e.g., time spent per session), and responsiveness (e.g., task \begin{table}
\begin{tabular}{c c c} \hline \hline \multirow{2}{*}{**Performance Group**} & \multicolumn{2}{c}{**Average Weekly**} & \multirow{2}{*}{**Engagement Increase (\%)**} \\  & **AI Interactions** & \\ \hline High Performers (Top 20\%) & 18.2 & 35\% \\ Moderate Performers (Middle 60\%) & 12.4 & 22\% \\ Low Performers (Bottom 20\%) & 6.3 & 8\% \\ \hline \hline \end{tabular} Note: Engagement increase is defined as the percentage growth in average weekly interactions (e.g., logins, feedback reviews, task completions) from the baseline (Week 1) to the study average, measured via system logs.  
\end{table} 
Table 8: Engagement metrics across performance groups. completion rates). For the experimental group, this included engagement with AI features like the Live Chat and AI Tutor, while the control group's engagement was tracked via attendance and participation logs. This granular data enabled the correlation between engagement levels and learning outcomes, as evidenced by the regression results. A linear regression analysis confirmed that higher AI engagement correlated positively with post-test improvements \(\left(R^{2}=0.76,\ p<0.001\right)\). Cognitive load was measured using NASA-TLX surveys before and after the intervention. Repeated measures of ANOVA were used to determine whether cognitive load levels decreased significantly. \[C_{loud}=\sum_{i=1}^{6}W_{i}\cdot\ R_{i}\]  
where:  
* \(C_{loud}\) = cognitive load score. * \(W_{i}\) = weight assigned to each factor (mental demand, physical demand, temporal demand, effort, frustration, performance). * \(R_{i}\) = raw rating of each factor. Results showed a 22% reduction in cognitive overload in the experimental group, compared to 6% in the control group. To evaluate long-term retention, delayed recall tests were conducted. A multiple linear regression model predicted retention scores:  
\[R_{ret}=\delta F_{adaptive}+\eta L+\lambda E\]  
where:  
* \(R_{ret}\) = retention rate. * \(F_{adaptive}\) = AI feedback score.