Table 4 Performance of the tests in simulation 4, H _0,B is false, H _0,A is false and f (Y|Y ≤ τ ∩ X = 1) and f (Y|Y ≤ τ ∩ X = 0) are identical (see Figure 3 for details of simulation).

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 90^th 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 90^th 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 90^th 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 90^th 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 90^th 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 90^th percentile.

0.619

0.365

0.726

0.553

0.852

0.704