Table 4: Estimated power of the two-stage procedure for different sample sizes and α pre
From: To test or not to test: Preliminary assessment of normality when comparing two independent samples
Strategy I | Strategy II | ||||||||||
|---|---|---|---|---|---|---|---|---|---|---|---|
n = 10 | n = 20 | n = 30 | n = 40 | n = 50 | n = 10 | n = 20 | n = 30 | n = 40 | n = 50 | ||
Exponential distributions with rate parameters 1.0 and 2.0 | |||||||||||
U test only | .224 | .443 | .612 | .743 | .835 | ||||||
α pre = .100 | .248 | .446 | .609 | .743 | .835 | .259 | .449 | .609 | .743 | .835 | |
α pre = .050 | .254 | .451 | .610 | .744 | .835 | .261 | .454 | .610 | .744 | .835 | |
α pre = .010 | .270 | .467 | .615 | .744 | .835 | .271 | .466 | .615 | .744 | .835 | |
α pre = .005 | .264 | .482 | .615 | .743 | .837 | .265 | .475 | .614 | .743 | .837 | |
t test only | .240 | .518 | .721 | .847 | .919 | ||||||
Uniform distributions in [0.0, 1.0] and [0.2, 1.2] | |||||||||||
U test only | .256 | .512 | .686 | .813 | .892 | ||||||
α pre = .100 | .287 | .537 | .703 | .817 | .894 | .290 | .529 | .697 | .816 | .895 | |
α pre = .050 | .292 | .550 | .714 | .821 | .894 | .294 | .542 | .702 | .817 | .894 | |
α pre = .010 | .295 | .558 | .740 | .848 | .908 | .295 | .559 | .729 | .835 | .900 | |
α pre = .005 | .294 | .561 | .749 | .855 | .915 | .295 | .563 | .742 | .842 | .906 | |
t test only | .292 | .561 | .748 | .867 | .930 | ||||||
Normal distributions with means 0.0 and 0.6 and unit variance | |||||||||||
U test only | .215 | .434 | .600 | .731 | .824 | ||||||
α pre = .100 | .244 | .455 | .626 | .750 | .840 | .249 | .459 | .631 | .754 | .843 | |
α pre = .050 | .245 | .456 | .625 | .753 | .842 | .248 | .459 | .628 | .755 | .844 | |
α pre = .010 | .244 | .455 | .629 | .756 | .842 | .245 | .455 | .630 | .756 | .842 | |
α pre = .005 | .245 | .458 | .627 | .751 | .845 | .246 | .458 | .628 | .752 | .845 | |
t test only | .247 | .456 | .627 | .754 | .844 | ||||||