# Feedback-Based Integration of the Whole Process of Data Anonymization in a Graphical Interface
## 2 sdcApp
### Risk/Utility
#### 2.4.3 Numerical risk measures  
The third block in the left navigation bar in the Risk/Utility tab provides information on risk and data utility for numerical key variables. The features are summarized in Table 9.  
In Compare summary statistics, it is possible to compare the distribution of the numerical key variables defined in the current SDC problem between the original and the anonymized data. This comparison is optionally also possibly for each level of a categorical key variable. To start, a numerical key variable needs to be selected from a drop-down field. Next to this input, another drop-down field is shown from which optionally may select one of the categorical key variables. Once the selections have been made, below the input fields some some important values such as the Pearson correlation coefficient using pairwise complete information, the standard deviations as well as the interquartile range and of the numerical key variable in the original and the anonymized dataset is displayed in a section named Measures.  
Below this information, two tables are presented where the first refers to the original and the second to the anonymized data. Both tables contain the extreme values, arithmetic mean and median as well as as the 5%-, 25%-, 75%-, and 95%-quantiles. In the case where a categorical variable has been chosen, these summary statistics are calculated for each level of the selected categorical key variable; otherwise, the summary statistics are computed over the entire dataset. We note that since the levels of  
\begin{table}
\begin{tabular}{l l} \hline \hline
**Feature** & **Description** \\ \hline Compare summary statistics & displays (summary) statistics for original and perturbed variables \\ Disclosure risk & displays a disclosure risk measures for numerical key variables \\ Information loss & shows two specific measures of information loss \\ \hline \hline \end{tabular}
\end{table}
Table 9: Risk measures and information for numerical key variablesthe categorical key variables might differ between original and anonymized dataset, it is not possible to show this information in a single table.  
If the link Disclosure Risk is chosen, it is possible to check on the estimated disclosure risk for the defined numerical key variables. The measure can be interpreted in the following way. In the original, unmodified data that has been used to create the SDC problem instance, the risk for the numeric key variables is assumed to be between 0% and 100%. The more data anonymization techniques such as microaggregation or adding noise are applied to the data, the less the upper bound of the risk will be. So users can compare the estimated upper bound of the risk for numerical key variables in the anonymized data and compare on how much it has reduced from the initial value of 100%. We note that the larger the deviations from the original data are, the lower the upper risk bound will be. However, this has of course also an impact on data utility measures that can be assessed from the menu button Information loss, which is the last choice in this tab.  
Clicking on Information loss, two measures of information loss, IL1s [14], and a robust measure based on differences in eigenvectors [15] for numerical key variables are shown. Generally, the more the numerical key variables are modified or rather anonymized, the higher the information loss values for both measures. We also note that information loss and the disclosure risk for numerical variables as discussed previously are always a trade of which need to be balanced.