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. Author manuscript; available in PMC: 2015 Jan 1.
Published in final edited form as: J Am Stat Assoc. 2014 Mar 19;109(505):275–287. doi: 10.1080/01621459.2013.844699

Table 2.

Quantitative comparison on the datasets under the six generating schemes. The averaged distances with standard deviations in parentheses are presented. Here n is changing from 50 to 200 and d is fixed to be 100.

Scheme n Pearson Sn Qn Kendall
Scheme 1 50 0.422(0.555) 0.607(0.473) 0.555(0.259) 0.473(0.266)
100 0.121(0.158) 0.188(0.140) 0.158(0.110) 0.140(0.201)
200 0.068(0.071) 0.072(0.072) 0.071(0.018) 0.072(0.024)

Scheme 2 50 0.911(0.878) 0.882(0.631) 0.878(0.105) 0.631(0.131)
100 0.806(0.715) 0.737(0.264) 0.715(0.169) 0.264(0.213)
200 0.484(0.354) 0.381(0.093) 0.354(0.222) 0.093(0.246)

Scheme 3 50 0.822(0.907) 0.921(0.473) 0.907(0.154) 0.473(0.101)
100 0.562(0.700) 0.737(0.140) 0.700(0.214) 0.140(0.202)
200 0.228(0.356) 0.410(0.072) 0.356(0.156) 0.072(0.255)

Scheme 4 50 0.947(0.679) 0.704(0.678) 0.679(0.095) 0.668(0.227)
100 0.910(0.247) 0.269(0.248) 0.247(0.157) 0.238(0.239)
200 0.873(0.079) 0.084(0.084) 0.079(0.232) 0.074(0.063)

Scheme 5 50 0.977(0.911) 0.910(0.854) 0.911(0.028) 0.854(0.102)
100 0.976(0.718) 0.722(0.532) 0.718(0.028) 0.532(0.214)
200 0.978(0.297) 0.305(0.147) 0.297(0.029) 0.147(0.244)

Scheme 6 50 0.959(0.848) 0.862(0.771) 0.848(0.060) 0.771(0.143)
100 0.931(0.548) 0.569(0.373) 0.548(0.108) 0.373(0.250)
200 0.840(0.156) 0.165(0.103) 0.156(0.223) 0.103(0.170)