Table 13: Hypothesis tests for mean differences of efficiency scores. Sample 1 is denoted as the “Control group” and sample 2 is denoted as the “Virtual group”.

Simulation 1Simulation 2Simulation 3Simulation 4
Control groupVirtual groupControl groupVirtual groupControl groupVirtual groupControl groupVirtual group

DEA
 Mean
 Variance
 Observations
 Pearson correlation
 Hypothesized mean difference
 Df14141414
Rank-sum test−3.09−3.21461.36881.7213
stat
P (T ≤ t)  two tail0.000120.000420.32660.1212
critical two tail

CCP efficiency evaluation
 Mean
 Variance
 Observations
 Pearson correlation
 Hypothesized mean difference
 Df14141414
Rank-sum test−1.8873−3.00722.1362.0117
stat
P (T ≤ t)   two tail0.0420.0050.00720.1041
critical two tail

DCF
 Mean
 Variance
 Observations
 Pearson correlation
 Hypothesized mean difference
 Df
Rank-sum test−1.8873−2.96571.86651.2236
stat
P (T ≤ t)   two tail0.053960.00590.086330.1682
critical two tail

The Rank-sum test shown previously is used to determine if the two samples being tested are of the same population. If they are of the same population, then we can conclude that the two frontiers for both the samples respectively, are one, and the same or that they consistently overlap one another, thus they can be assumed to be of the same surface.