## 3 Results
### Detection
#### 3.1.2 Realistic Setting--Dataset
The \(p\)-value is computed between the Standard Positioning and each of the other positions; hence, the value is not present in the column related to the Standard Positioning. Figure 13 shows the percentage of anomalies for each experimental configuration at different values of the _contamination_ parameter, split per difficulty level (Easy--Hard). Each point on the curve represents the percentage of records within the subset (i.e., the value on the X-axis) identified as having a shift in the data compared to control data. The statistical analysis revealed that when comparing the percentages of values with covariate shift in the standard position and in a different position, the \(p\)-values are consistently significant, except for a few cases where the contamination level in training is 1%. However, a different scenario emerges when comparing the values obtained in the standard position with those in a similar position, as achieving significant results requires a high level of contamination in training, specifically exceeding 30%. The following three tables (Tables 8-10) display the percentage values of records identified as covariate shifts, using a contamination level of 30% and dividing the data into Hard and Easy, as presented graphically in Figure 13. In the tables, alongside the information regarding the percentage of records, the Wilcoxon \(p\)-value is provided. This \(p\)-value is calculated by comparing the values of the test configuration with those of the control configuration. \begin{table}
\begin{tabular}{c c c c c c c} \hline  & \multicolumn{2}{c}{**Standard Positioning**} & \multicolumn{2}{c}{**Similar Positioning**} & \multicolumn{2}{c}{**Different Positioning**} \\ \hline
**Second** & **Accuracy** & \(p\)**-Value** & **Accuracy** & \(p\)**-Value** & **Accuracy** & \(p\)**-Value** \\ \hline
10 & 0.82 & - & 0.78 & 0.23 & 0.66 & \(1\times 10^{-3}\) \\
30 & 0.86 & - & 0.8 & 0.23 & 0.67 & \(1\times 10^{-3}\) \\
60 & 0.85 & - & 0.79 & 0.28 & 0.66 & \(1\times 10^{-3}\) \\ \hline \end{tabular}
\end{table} 
Table 7: Classification accuracy values and \(p\)-values achieved across configurations. Figure 12: Mean Accuracy across all tests for each configuration and the corresponding Wilcoxon test. The test compares control condition (Standard Positioning) values with the other two configurations. The dashed orange line represents the \(p\)-value of the Wilcoxon test comparing accuracy in the control and ‘Different Positioning’ configurations. The green dashed line for ‘Standard Positioning’ versus ‘Similar Positioning’ is not visible, exceeding the 0.15 Y-axis limit for every decimation value. All \(p\)-values are below \(10^{-7}\). The dashed grey line indicates the significance level chosen for the test (i.e., 0.05). Figure 13: Each graph pair on a row represents a distinct isolation forest model trained with a different contamination level, using the Hard and Easy condition data. Each curve point indicates the percentage of records within the subset (X-axis) identified with data shift compared to the control. Wilcoxon tests at the graph bottoms show _p_-values, comparing %CS values of the control with the other two configurations. The dashed grey line indicates the significance level chosen for the test (i.e., 0.05). \begin{table}
\begin{tabular}{c c c c c} \hline \hline  & \multicolumn{2}{c}{**Hard**} & \multicolumn{2}{c}{**Easy**} \\ \hline
**N Record** & **\%CS** & _p_**-Value** & **\%CS** & _p_**-Value** \\ \hline
10 & 0.38 & - & 0.37 & - \\
15 & 0.37 & - & 0.36 & - \\
20 & 0.35 & - & 0.35 & - \\
30 & 0.34 & - & 0.37 & - \\
45 & 0.33 & - & 0.36 & - \\
60 & 0.34 & - & 0.36 & - \\ \hline \hline \end{tabular}
\end{table} 
Table 8: Standard Positioning.