Programmatic efficiency comparisons between unequally sized groups of decision-making units in data envelopment analysis

Data envelopment analysis (DEA) is a popular non-parametric technique for determining the efficiency of a homogeneous set of decision-making units (DMUs). In many practical cases, there is some doubt if all the DMUs form a single group with a common efficiency distribution. The Mann–Whitney rank statistic has been used in DEA both to test if two groups of DMUs come from a common efficiency distribution and also to test if the two groups have a common frontier, each of which are likely to have important but different policy implications for the management of the groups. In this paper it is demonstrated that where the Mann–Whitney rank statistic is used for the second of these it is likely to overestimate programmatic inefficiency, particularly of the smaller group. A new non-parametric statistic is proposed for the case of comparing the efficient frontiers of two groups, which overcomes the problems we identify in the use of the Mann–Whitney rank statistic for this purpose.