A cautionary note on methods of comparing programmatic efficiency between two or more groups of decision making units in data envelopment analysis

In some applications of data envelopment analysis (DEA) there may be doubt as to whether all the DMUs form a single group with a common efficiency distribution. The Mann–Whitney rank statistic has been used to evaluate if two groups of DMUs come from a common efficiency distribution under the assumption of them sharing a common frontier and to test if the two groups have a common frontier. These procedures have subsequently been extended using the Kruskal–Wallis rank statistic to consider more than two groups. This technical note identifies problems with the second of these applications of both the Mann–Whitney and Kruskal–Wallis rank statistics. It also considers possible alternative methods of testing if groups have a common frontier, and the difficulties of disaggregating managerial and programmatic efficiency within a non-parametric framework.