DEA non-parametric ranking test and index measurement: slack-adjusted DEA and an application to Japanese agriculture cooperatives

This article describes a new DEA (data envelopment analysis) ranking approach that combines efficiency analysis (by DEA) with index measurement (by DEA sensitivity analysis). The sensitivity analysis, incorporated into the index measurement, omits an efficient DMU (decision making unit) to obtain the index numbers of all the DMUs. The proposed DEA ranking approach is theoretically linked to a non-parametric rank sum test. Using the rank sum test, this article statistically examines whether two groups of DMUs have different distribution functions of efficiency. As an illustrative case study, this article applies the proposed approach to Japanese Agriculture Cooperatives.