## 4.
### Data Analysis and Statistical Methods
#### 3.5.1 Descriptive Statistics and Data Normalization  
Before conducting inferential statistical analyses, descriptive statistics were calculated to summarize participant performance across different feedback conditions (AI-driven vs. instructor-led). From Table 7, the experimental group receiving AI-driven adaptive feedback showed a 28% improvement in conceptual mastery, while the control group exhibited a 14% increase, suggesting that AI-driven interventions enhance learning outcomes more effectively than traditional feedback mechanisms. The pre- and post-tests summarized in Table 6 were administered across the study's focal themes: Computer Science (e.g., variables, loops), Mathematics (e.g., linear equations), Physics (e.g., Newton's laws), and English Language (e.g., essay writing, syntax). Each assessment, consisting of 50 questions (70% multiple-choice, 30% short-answer), was designed to take approximately 60 min to complete. This duration was determined through pilot testing to ensure comprehensive evaluation of conceptual mastery and applied understanding within a practical timeframe, consistent across all themes for both the experimental and control groups. In the study, \"feedback effectiveness\" is defined as the capacity of AI-driven adaptive feedback to improve conceptual mastery, enhance student engagement, increase knowledge retention, and reduce cognitive overload, tailored to the needs of struggling learners in mixed-ability classrooms. It was measured through a combination of quantitative and qualitative indicators: (1) improvement in conceptual mastery, calculated as the percentage increase in pre- to post-test scores; (2) engagement levels, assessed via the frequency and quality of student interactions with the AI system (e.g., average weekly interactions); (3) retention rates, evaluated through delayed recall test scores administered four weeks post-intervention; and (4) cognitive overload reduction, quantified using NASA-TLX survey responses. These metrics were triangulated with qualitative data from student surveys on perceived feedback usefulness (Likert-scale ratings) and instructor observations to ensure a comprehensive evaluation of effectiveness across diverse learning dimensions. To ensure the validity of our inferential analyses, data normalization was performed. Outliers were detected using \(Z\)-score normalization:  
\[Z=\frac{X-\mu}{\sigma}\]  
where: \begin{table}
\begin{tabular}{c c c c} \hline \hline
**Group** & **Pre-Test** & **Post-Test** & **Improvement (\%)** \\  & **Mean (SD)** & **Mean (SD)** & **Improvement (\%)** \\ \hline Experimental (AI-Driven & 52.4 (\(\pm\)12.3) & 80.2 (\(\pm\)10.4) & 28\% \\ Feedback, \(n\) = 350) & 51.8 (\(\pm\)11.7) & 65.2 (\(\pm\)9.8) & 14\% \\ \hline \hline \end{tabular} Note: Pre- and post-tests covered STEM themes (Computer Science: programming fundamentals; Mathematics: algebra; Physics: mechanics) and Language Education (English: grammar, vocabulary, composition). Each test lasted approximately 60 min.  
\end{table} 
Table 7: Descriptive statistics of pre- and post-test scores. * \(X\) = raw score. * \(\mu\) = mean. * \(\sigma\) = standard deviation. Score with \(Z>3\) were considered outliers and excluded from further analysis. To evaluate the impact of AI-driven feedback on conceptual mastery, a paired \(t\)-test was used within each group, and an independent \(t\)-test was applied to compare post-test scores between groups. \[t=\frac{\overline{X}_{1}-\overline{X}_{2}}{S_{p}\sqrt{\frac{1}{n_{1}}+\frac{1} {n_{2}}}}\]  
where:  
* \(\overline{X}_{1},\ \overline{X}_{2}\) = mean scores for pre- and post-tests. * \(S_{p}\) = pooled standard deviation. * \(n_{1},\ n_{2}\) = sample sizes. The AI-driven group showed a statistically significant improvement, confirming that adaptive feedback enhances learning outcomes.