A Distribution-Free Approach to Stochastic Efficiency Measurement with Inclusion of Expert Knowledge

Table 16

Statistical analysis for frontier comparisons. Observed DMUs are evaluated against the 3 different frontiers to determine their efficiency scores which are calculated using the normal DEA model and to determine if the efficiency scores for each group are substantially different when comparing EFF to DEA, EFF to DCF, and EFF to CCP.

	Exp.grp+; EFF	Exp.grp+; DEA	Exp.grp+; EFF	Exp.grp+; DCF	Exp.grp+; EFF	Exp.grp+; CCP
Simulation 1
Mean	0.852	0.899	0.852	0.885	0.852	0.887
Variance	0.01396	0.01355	0.01396	0.01389	0.01396	0.01376
Observations	15	15	15	15	15	15
Pearson correlation	0.922		0.87986		0.881
Hypothesized mean difference	0		0		0
Df	14		14		14
Rank-sum test	1.2858		0.9125		0.9125
𝑡 stat	−3.9644		−2.2335		−2.3537
P (T ≤ t)   two tail	0.0014		0.04235		0.03372
𝑡 critical two tail	2.145		2.145		2.145
Simulation 2
Mean	0.875	0.922	0.875	0.908	0.875	0.908
Variance	0.01272	0.01242	0.0127	0.0115	0.0127	0.0115
Observations	15	15	15	15	15	15
Pearson correlation	0.94071		0.8875		0.8918
Hypothesized mean difference	0		0		0
Df	14		14		14
Rank-sum test	1.3066		0.9747		1.0162
𝑡 stat	−4.6604		−2.3984		−2.487
P (T ≤ t)   two tail	0.00037		0.031		0.02611
𝑡 critical two tail	2.145		2.145		2.145
Simulation 3
Mean	0.92	0.933	0.92	0.916	0.92	0.902
Variance	0.00879	0.00815	0.00879	0.00806	0.00879	0.0077
Observations	15	15	15	15	15	15
Pearson; correlation	0.95301		0.8804		0.9082
Hypothesized mean difference	0		0		0
Df	14		14		14
Rank-sum test	0.7259		−0.0622		−0.6014
𝑡 stat	−1.8125		0.29423		1.68719
P (T ≤ t)   two tail	0.0914		0.7729		0.1137
𝑡 critical two tail	2.145		2.145		2.145
Simulation 4
Mean	0.882	0.904	0.882	0.887	0.882	0.868
Variance	0.0153	0.0173	0.0153	0.0184	0.0153	0.0162
Observations	15	15	15	15	15	15
Pearson correlation	0.9425		0.905		0.8996
Hypothesized mean difference	0		0		0
Df	14		14		14
Rank-sum test	0.8503		0.1452		−0.394
𝑡 stat	−1.9248		−0.312		1.0043
P (T ≤ t)   two tail	0.0748		0.7599		−0.312
𝑡 critical two tail	2.145		2.145		2.145