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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