## 4 Results
The lowest results were from direct transfer from individual model 3 (the smallest), with a drop of \(-4.14\%\), along with the voting approach and the federated approach with drops of \(-0.48\%\) and \(-3.63\%\), respectively. The left side of Figure 15 shows the AUC results when the target was the third dataset, which was the smallest, with only 16,000 examples. The results were different and higher than those of the two previous target datasets. The AUC values ranged between 0.8850 and 0.8458. These results showed that in that dataset, the local bias was higher. This is reflected in the performance of the baseline, which was the best model, with an AUC of 0.8849 \(\pm\) 0.0075. The repurposed and stacked transferred learning models again produced the highest AUC values of about 0.88. However, the centralized approach produced the lowest AUC values (0.84), showing that it did not work very well when applied to a small target dataset. The model transferred directly from the first, large dataset produced the second lowest value (0.85), and the model transferred from the second, medium dataset  
Figure 15: (**a**) AUC and (**b**) \(\Delta\)AUC for all approaches. Target: 3 rd entity dataset. worked a little better (0.86). Finally, the voting and federated approaches produced very similar results with AUC values of about 0.86. The right side of Figure 15 shows the increase or decrease in AUC for the third target dataset. In that case, all the approaches showed a decrease in AUC. The largest drop was produced by the centralized (\(-3.92\%\)) and direct approaches (\(-3.49\%\) and \(-2.29\%\)). In contrast, the repurposed approach performed well on that dataset with a drop of only \(-0.12\%\) from the first dataset and \(-0.35\%\) from the second. The stacked approach also gave good results with a drop of \(-0.42\%\). Furthermore, the soft-voting and federated-voting models gave even worse results but with a smaller difference (\(-1.75\%\) and \(-2.04\%\), respectively) than for the two previous cases using entities 1 and 2 as targets). Finally, we carried out two tests to verify whether the differences in AUC were statistically significant. To achieve that, we conducted a paired t-test and a z-test with alpha = 0.05 (see Table 2) to analyze significant differences between the performance of the approaches evaluated versus our baseline (individual model) in terms of AUC, using the individual course dataset as a target. A \(p\)-value of 0.05 or less indicated that the difference was significant. We used these two specific tests because they had been proposed as statistical analysis in other related works [15; 16] to find any significant differences between these machine learning approaches. As Table 2 shows, the \(p\)-values of the two tests (Z-test and \(T\)-test) confirmed the same results. The only approaches that produced significant differences in the three target dataset cases were direct transfer, soft voting, and federated learning. These approaches produced the lowest performance in AUC, and these differences with the baseline model were statistically significant indicating a real drop in performance. With the other approaches, we identified no significant differences when using the centralized approach compared to the individual model in the first and second entities (\(p>0.05\)), demonstrating that merging data from numerous entities does not decrease