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Table 2 Performance of the tests in simulation 2, H 0,A is true, H 0,B is false and f (Y|YτX = 1) is radically different from f (Y|YτX = 0) (see Figure 3 for details of simulation).

From: Testing for differences in distribution tails to test for differences in 'maximum' lifespan

Test Sample Size (N) Per Group
  50 80 100
  α = .05 α = .01 α = .05 α = .01 α = .05 α = .01
Tests of H 0, A (Wang-Allison tests)
QT3 with τ set to 130. 0.032 0.008 0.041 0.006 0.040 0.006
QT3 with τ set to sample 90th percentile. 0.034 0.034 0.104 0.009 0.062 0.018
QT4 with τ set to 130. 0.038 0.008 0.051 0.009 0.047 0.007
QT4 with τ set to sample 90th percentile. 0.034 0.034 0.104 0.033 0.062 0.018
Tests of H 0, B
Wilcoxon-Mann-Whitney with τ set to 130. 0.264 0.090 0.504 0.261 0.631 0.368
Wilcoxon-Mann-Whitney with τ set to sample 90th percentile. 0.16 0.051 0.314 0.143 0.406 0.220
Permutation test with τ set to 130 0.337 0.111 0.608 0.332 0.737 0.456
Permutation test with τ set to sample 90th percentile. 0.197 0.047 0.423 0.204 0.525 0.284
Tests of H 0, C (new tests)
Wilcoxon-Mann-Whitney with τ set to 130. 0.051 0.008 0.062 0.012 0.056 0.010
Wilcoxon-Mann-Whitney with τ set to sample 90th percentile. 0.107 0.029 0.090 0.028 0.124 0.035
Permutation test with τ set to 130. 0.061 0.013 0.055 0.012 0.065 0.014
Permutation test with τ set to sample 90th percentile. 0.109 0.032 0.097 0.03 0.129 0.046