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Table 4 Performance of the tests in simulation 4, H 0,B is false, H 0,A is false and f (Y|YτX = 1) and f (Y|YτX = 0) are identical (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. 0.244 0.101 0.412 0.181 0.490 0.258
QT3 with τ set to sample 90th percentile. 0.363 0.363 0.735 0.337 0.753 0.600
QT4 with τ set to 130. 0.266 0.102 0.418 0.187 0.514 0.274
QT4 with τ set to sample 90th percentile. 0.363 0.363 0.735 0.555 0.753 0.600
Tests of H 0, B
Wilcoxon-Mann-Whitney with τ set to 130. 0.409 0.172 0.684 0.411 0.804 0.56
Wilcoxon-Mann-Whitney with τ set to sample 90th percentile. 0.245 0.142 0.33 0.144 0.434 0.176
Permutation test with τ set to 130. 0.517 0.244 0.81 0.568 0.913 0.728
Permutation test with τ set to sample 90th percentile. 0.169 0.039 0.428 0.190 0.569 0.249
Tests of H 0, C (new tests)
Wilcoxon-Mann-Whitney with τ set to 130. 0.374 0.171 0.528 0.280 0.629 0.373
Wilcoxon-Mann-Whitney with τ set to sample 90th percentile. 0.602 0.353 0.734 0.552 0.865 0.724
Permutation test with τ set to 130. 0.393 0.177 0.524 0.288 0.626 0.377
Permutation test with τ set to sample 90th percentile. 0.619 0.365 0.726 0.553 0.852 0.704