The Receiver Operating Curve is a graph of the significance level of the test (false alarm rate)
against the power of the test (1- the misdetect rate). For the five different test statistics
we have been examining, the ROC curve is shown below.
The Receiver Operating Curve for the Five Test Statistics
By examining the graph we see that the ordering is uniform.For any significance of test, the ordering from best to worst is: Min, Harmonic Mean, Geometric Mean, Arithmetic Mean, Max. As expected the minimum of the closest interpoint distances did, as expected, better than the maximum of the interpoint distances.