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

Table 2 Performance of the tests in simulation 2, H _0,Ais true, H _0,Bis false and f (Y|Y ≤ τ ∩ X = 1) is radically different from f (Y|Y ≤ τ ∩ X = 0) (see Figure 3 for details of simulation).

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 90^th 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 90^th 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 90^th 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 90^th 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 90^th 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 90^th percentile.	0.109	0.032	0.097	0.03	0.129	0.046

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