# Detecting Bid-Rigging in Public Procurement. A Cluster Analysis Approach
## 4 Discussion of the Results  
The existence of the two clusters indicates a certain \"gap\" or discontinuity in data. This discontinuity occurs at auctions where price growth is over 15% in 2016-2017 compared to 2015-2016. Most maintenance contracts for snow removal have a 20-40% increase in value in the 2016-2017 winter season compared to that of 2015-2016. Regarding the actual price paid per km of snow removal, the increases of percentages were set between 49% to 175% (in the analyzed period), which may not be economically reasonable.  
From the cluster analysis on the percentage increases between the actual price and the contractual price per designated km in the two analyzed seasons (winter 2015-2016 and winter 2016-2017), it follows that there is a category of contracts with a normal (Gaussian) value and another category of contracts that do not follow such data distribution. This indicates that auctions in the second cluster could raise some suspicions about the organization/performance of these award procedures. The lots/SDNs in this category are found in Figure A2 of Appendix A.  
\begin{table}
\begin{tabular}{c c c c c c c} \hline \hline  & \multicolumn{2}{c}{**Kolmogorov–Smirnov a**} & \multicolumn{3}{c}{**Shapiro–Wilk**} \\ \cline{2-7}  & **Statistic** & **df** & **Sig.** & **Statistic** & **df** & **Sig.** \\ \hline Cluster 1 & 0.234 & 28 & 0.000 & 0.834 & 28 & 0.000 \\ Cluster 2 & 0.305 & 13 & 0.062 & 0.744 & 13 & 0.096 \\ \hline \hline \end{tabular}  
* This is a lower bound of the true significance. Liliefcore significance correction. Source: own computation in SPSS.  
\end{table}
Table 8: Test of Normality.  
Figure 6: Box-plot cluster. Source: own processing using SPSS software.  
We also note a discontinuity in the data as far as it concerns the contract prices per km of snow in the 2016-2017 season, compared to 2015-2016. This discontinuity appears in contracts whose value has increased by over 15% (with a maximum increase of 104%) (Figure A1 in Appendix A). This is a confirmation through the statistical analysis that there have been certain award procedures where the increase in the price paid per kilometer of snow can raise some suspicions about the organization/running of these award procedures. Lots/SDNs in this category can be found in Figures A1 and A2 of Appendix A.  
We may conclude, based on the testing of the statistical assumptions, that there was a significant difference between the contractual price and the actual per km of snow, both for the winter 2015-2016 and for winter 2016-2017 (Table 2). In addition, there are significant differences in terms of both statistics and in terms of the actual price paid per km over the 2016-2017 season compared to 2015-2016 (Figures A3 and A4 from Appendix A). These results show that we may be in the presence of an anticompetitive practice/agreement/bidrigging regarding the results of the procedures for the snow removal auctions for the period 2016-2017.  
The econometric analyses used in our study (Sections 3.1-3.3) supported the findings of a cartel agreement. Cluster analysis, statistical hypothesis, normality and symmetry and nonparametric tests reveal two types of auctions during the analyzed period: competitive and noncompetitive bids.