## 3 Results
### Correction
#### 3.2.1 Laboratory Setting  
Dataset  
Figure 14 shows the Accuracy values achieved using the RF model trained on the control data, pre and post-application of the correction method. In particular, the dashed line is referred to as the accuracy pre-shift correction, and the continuous line is referred to as the post-shift correction. It can be easily observed that, for the _\"Test diff Ref diff Chs\"_ configuration, the accuracy values curve increases at each decimation step after data correction through the transformation function. However, this transformation does not appear to have yielded improvements in the other configurations affected by shifts. The statistical analysis reveals that all the comparisons made appear to be statistically significant, as for all decimation levels and all three Wilcoxon curves, the \(p\)-values fall below the 0.05 threshold. The [PERSON]'s test calculated between pre- and post-correction values using the test configuration _\"Test diff Ref diff Chs\"_ demonstrates a value exceeding 6, indicating a strong and significant difference between the means of the two distributions. Additionally, notable differences are observed in the distributions of the other two tests, with values of 4.26 (_\"Test diff Ref same Chs\"_) and 3.57 (_\"Test same Ref diff Chs\"_), respectively.  
Table 11 compares the accuracy values achieved pre- and post-correction for some selected decimation values for all configurations except the Control one. For each comparison, the Wilcoxon \(p\)-value is also reported.  
Figure 15 shows the values (in %) of records identified with covariate shift at different values of contamination, using a subsample of the first 15 records in each test condition. The values achieved pre and post-application of the correction function are also compared. The Wilcoxon statistical test is calculated by comparing the values in the test conditions achieved pre- and post-correction. The curves related to the comparison between pre- and post-correction values indicate that, concerning the _\"Test diff Ref diff Chs\"_ configuration, the \(p\)-values consistently remain significant (<0.05). In contrast, for the other two comparisons in the different configurations, statistically significant results are only achieved when using a contamination level of 1% or 40%.  
\begin{table}
\begin{tabular}{c c c c c} \hline \hline  & **Hard** & & **Easy** \\ \hline
**N Record** & **\%CS** & \(p\)-Value** & **\%CS** & \(p\)-Value** \\ \hline
10 & 0.55 & \(1\times 10^{-3}\) & 0.53 & \(5\times 10^{-3}\) \\
15 & 0.55 & \(5\times 10^{-3}\) & 0.51 & \(3\times 10^{-3}\) \\
20 & 0.54 & \(5\times 10^{-3}\) & 0.49 & \(3\times 10^{-3}\) \\
30 & 0.55 & \(5\times 10^{-3}\) & 0.50 & \(3\times 10^{-3}\) \\
45 & 0.53 & \(1\times 10^{-3}\) & 0.51 & \(3\times 10^{-3}\) \\
60 & 0.53 & \(1\times 10^{-3}\) & 0.52 & \(3\times 10^{-3}\) \\ \hline \hline \end{tabular}
\end{table}
Table 10: Similar Positioning.  
\begin{table}
\begin{tabular}{c c c c c} \hline \hline  & **Hard** & & **Easy** \\ \hline
**N Record** & **\%CS** & \(p\)-Value** & **\%CS** & \(p\)-Value** \\ \hline
10 & 0.46 & 0.1 & 0.42 & 0.37 \\
15 & 0.45 & 0.02 & 0.41 & 0.69 \\
20 & 0.45 & 0.01 & 0.42 & 0.43 \\
30 & 0.46 & \(1\times 10^{-3}\) & 0.44 & 0.16 \\
45 & 0.44 & \(1\times 10^{-3}\) & 0.45 & \(1\times 10^{-3}\) \\
60 & 0.45 & \(1\times 10^{-3}\) & 0.46 & \(1\times 10^{-3}\) \\ \hline \hline \end{tabular}
\end{table}
Table 9: Similar Positioning.