## 5 Simulation Results and Discussion
As shown in Table 2, the Z-score method using the MAD as a scale estimator identified at least 50% of the observations in each dataset as outliers. On the other hand, the Z-score method with the \(S_{n}\) scale estimator identified, on average, 13% of the observations in each dataset as outliers. This implies that the Z-score method based on the MAD scale estimator considered several valid RSS observations as outliers, demonstrating its inefficiency when applied to time-series RSS observations. A number of factors could contribute to such inefficiency. The first one includes the previously mentioned high gross error sensitivity. The second is its symmetrical approach to detecting outliers from observation medians, which is inefficient when applied to an asymmetrical observation, such as time-series RSS observations. There were no clearly visible outliers in the datasets used to evaluate the performance of the outlier detection methods earlier. To further demonstrate the \(S_{n}\) scale estimator's outlier detection capability, artificial outliers are deliberately inserted into two of the datasets, namely, datasets 2 and 4. This is achieved by replacing some of the valid RSS observations with artificial outliers. Figures 11 and 12, respectively, show the RSS datasets 2 and 4 with and without the artificial outliers. The artificial outliers are marked with the colour red. In Figure 11, all the artificial outliers are inserted in such a way that they are visually alien to the observations. In Figure 12, one of the artificial outliers is placed very close to an RSS observation. If the outlier detection method considers the RSS observation to be a non-outlier observation, it is expected that the artificial outlier will also be considered a non-outlier observation due to its close proximity to the RSS observation. \begin{table}
\begin{tabular}{c c c c c} \hline \hline \multirow{2}{*}{**RSS Dataset**} & \multicolumn{2}{c}{\(S_{n}\) Scale Estimator} & \multicolumn{2}{c}{**MAD Scale Estimator**} \\ \cline{2-5}  & **No. of Outlier** & **\% of Total** & **No. of Outlier** & **\% of Total** \\  & **Detected** & **Observation** & **Detected** & **Observation** \\ \hline
1 & 4 & 13 & 23 & 72 \\
2 & 6 & 19 & 16 & 50 \\
3 & 0 & 0 & 14 & 44 \\
4 & 2 & 6 & 11 & 34 \\
5 & 8 & 25 & 32 & 100 \\
6 & 7 & 22 & 11 & 34 \\
7 & 6 & 19 & 10 & 31 \\
8 & 0 & 0 & 20 & 63 \\ \hline \hline \end{tabular}
\end{table} 
Table 2: Comparison of the number of detected outliers. Figure 10: RSS outlier detection comparison for RSS Dataset 8. (**a**) \(S_{n}\) scale estimator, and (**b**) MAD scale estimator. Figures 13 and 14 show, respectively, the outlier detection performance comparisons of the Z-score method with MAD and \(S_{n}\) as scale estimators for the RSS datasets taken into consideration with and without the artificial outliers. From Figure 13, both the \(Z\)-score methods using the \(S_{n}\) and MAD scale estimators did not consider the artificial outliers as valid RSS observations, which is what is expected. However, in Figure 14, the \(Z\)-score method with the \(S_{n}\) scale estimator considered one of the artificial outliers that is close to the valid RSS observation as a non-outlier observation. This is expected, as the distance between the artificial outlier and the valid RSS observation is not large enough to consider it an outlier. It can be recalled that the \(S_{n}\) scale estimator uses the distance between pairs of observations to classify them as outliers. This is different from the MAD scale estimator, which uses the distance between an observation and the median of the observations to detect outliers. Hence, it considered the artificial outlier, which was close to the valid RSS observation, an outlier as it was very far from the median of the observation. Even though outliers have been removed from the observations, it is possible that the observations are skewed. As a result, it is recommended that the median approach be used to determine the RSS observation representative.