# Economies of Scale and Efficiency in the Wastewater Treatment Sector: A Decision Tree Approach
## 4 Results
### Efficiency Analysis of the Global Sample with the EAT Approach  
First, the efficiency scores for the 362 WWTPs were calculated following the EAT model using variable returns to scale [57], which allowed for a comparison of each unit analyzed, with the units having a similar size (see Table 4). The EAT model results show that Group 4 (treating wastewater above 50,000 P.E. ), which includes 23 WWTPs, obtained the greatest average efficiency score, with an efficiency index of 0.54. This value is followed by the one obtained by Group 3 (treating wastewater between 20,000 and 50,000 P.E. ), which consists of 21 WWTPs, with an average efficiency score of 0.40. Then, Group 2 (treating wastewater between 10,000 and 20,000 P.E. ), which comprises 23 WWTPs, has an average efficiency score of 0.30. Finally, Group 1 (treating fewer than 10,000 P.E. ), including 295 WWTPs (the largest group), is the least efficient group, with an average efficiency score of 0.15. These results demonstrate that the increase in the efficiency of WWTPs is directly linked to the P.E. that the WWTPs treat. Therefore, as the P.E. of the WWTP increases, the unit economic costs for wastewater treatment decrease. These findings are consistent with the results obtained in other studies [16; 28; 58; 59; 60], in that bigger WWTPs work more efficiently than smaller ones; an increase in WWTP size incurs lower unitary production costs. In view of these results, the wastewater treatment process presents opportunities for saving by reducing the average cost (EUR/P.E.). This information can be highly useful in the design of more efficient WWTPs in terms of reducing costs and obtaining treated water of a suitable quality. The novelty of the current study, compared to the studies mentioned previously, lies in its more exhaustive analysis, since a greater number of output variables were considered. Extending the study to include the elimination of nutrients (TN and TP) allows us to obtain more complete results that confirm that economies of scale are not only obtained for the main pollutants. However, it is necessary to study subgroups in order to identify the possible existence of an optimal minimum size. Although the results obtained show that there is a clear relationship between the efficiency score of the WWTP groups and the costs per P.E., it is worth checking that the differences between them are statistically significant. The results of the Kruskal-Wallis test are shown in Table 4. With a significance of 5%, the null hypothesis can be rejected. Therefore, we can accept that the differences between the four groups are significant. To become more efficient, the WWTPs belonging to Group 1 need an average reduction in all costs. In terms of efficiency, the score obtained is 0.15, which implies a high capacity for improvement. However, an increase in the size of the plants (from Group 1 to Group 2) would increase the score obtained and allow them to achieve an average of 0.29. Group 2 increases the score to 0.29: this result implies a decrease in the economic costs of the treatment, as well as the improved elimination of pollutants. Again, Group 2 could increase the obtained efficiency to 0.39 (Group 3) if the facilities were increased in size \begin{table}
\begin{tabular}{c c c c c} \hline \hline
**Group** & **Number of WWTPs** & **Average Efficiency Score** & **Score** \\ \hline
1 & 295 & 0.1509 & & \\
2 & 23 & 0.2995 & Chi-square & 90.3972347 \\
3 & 21 & 0.3980 & df & 3 \\
4 & 23 & 0.5393 & Asymp. Sig & 0.000 \\ Total & 362 & & & \\ \hline \hline \end{tabular}
\end{table} 
Table 4: Average efficiency scores for the four groups with variable returns to the scale model (EAT). Kruskal-Wallis test results for the four groups. according to the treated P.E. Group 3 shows similar behavior, obtaining an efficiency score of 0.39, which implies a reduction in economic costs as well as an increase in pollutant removal, but this score is lower than that of Group 4, which obtains 0.52, indicating a much better performance.