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. Author manuscript; available in PMC: 2017 Sep 7.
Published in final edited form as: Stat Biopharm Res. 2014 May 27;6(4):289–301. doi: 10.1080/19466315.2014.923325

Table 2.

Simulated empirical type I error (α) and power (1 − β) based on 100,000 simulation runs for the Weibull and log-normal distributions with the reduced sample size, adjusting the empirical power of Z1 to nearly 80%, for fixed tests with Z1 − Z3

Dist. Design 0.2 vs 0.35 0.2 vs 0.4 0.3 vs 0.45
W(ω, κ) κ Test n α 1 − β n α 1 − β n α 1 − β
0.5 Z1 56 .055 .800 33 .057 .806 70 .051 .808
Z2 56 .057 .807 33 .061 .815 70 .056 .822
Z3 56 .070 .830 33 .073 .841 70 .062 .833
1 Z1 58 .054 .803 34 .056 .802 72 .052 .807
Z2 58 .059 .810 34 .060 .814 72 .057 .821
Z3 58 .072 .831 34 .075 .843 72 .063 .831
2 Z1 60 .055 .802 35 .055 .806 74 .052 .808
Z2 60 .058 .810 35 .059 .814 74 .057 .819
Z3 60 .069 .833 35 .074 .842 74 .062 .833
LN(μ, σ2) κ Test n α 1 − β n α 1 − β n α 1 − β
2 Z1 56 .055 .801 33 .055 .804 70 .052 .806
Z2 56 .057 .807 33 .060 .815 70 .058 .820
Z3 56 .070 .830 33 .074 .838 70 .063 .832
1 Z1 58 .054 .799 34 .056 .802 72 .051 .805
Z2 58 .058 .810 34 .059 .812 72 .057 .817
Z3 58 .070 .831 34 .075 .841 72 .062 .829
0.5 Z1 60 .055 .802 35 .057 .804 74 .051 .805
Z2 60 .056 .809 35 .058 .811 74 .057 .817
Z3 60 .070 .831 35 .073 .839 74 .062 .831
Dist. Design 0.5 vs 0.65 0.6 vs 0.75 0.7 vs 0.8
W(ω, κ) κ Test n α 1 − β n α 1 − β n α 1 − β
0.5 Z1 75 .048 .805 68 .046 .806 132 .047 .807
Z2 75 .058 .830 68 .059 .839 132 .058 .837
Z3 75 .054 .826 68 .052 .821 132 .050 .819
1 Z1 77 .048 .805 70 .047 .804 136 .046 .801
Z2 77 .057 .830 70 .059 .837 136 .058 .833
Z3 77 .055 .822 70 .052 .821 136 .050 .811
2 Z1 80 .048 .808 72 .046 .801 139 .046 .801
Z2 80 .058 .830 72 .058 .835 139 .058 .833
Z3 80 .055 .826 72 .053 .820 139 .049 .813
LN(μ, σ2) κ Test n α 1 − β n α 1 − β n α 1 − β
2 Z1 75 .048 .801 68 .046 .796 132 .047 .797
Z2 75 .058 .826 68 .062 .832 132 .058 .826
Z3 75 .056 .821 68 .053 .814 132 .050 .808
1 Z1 77 .048 .799 70 .045 .792 136 .047 .795
Z2 77 .058 .823 70 .059 .830 136 .058 .826
Z3 77 .055 .814 70 .052 .813 136 .050 .805
0.5 Z1 80 .048 .803 72 .046 .792 139 .046 .792
Z2 80 .058 .827 72 .060 .828 139 .057 .825
Z3 80 .055 .819 72 .053 .812 139 .051 .807