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Table 2 The true Prob(X<Y) for each scenario in the simulation study

From: t-tests, non-parametric tests, and large studies—a paradox of statistical practice?

  Gamma distributions   Lognormal distributions
  Skewness   Skewness
Std.ratio 1.0 2.0 3.0 4.0   1.0 2.0 3.0 4.0
1.05 0.50 0.51 0.54 0.58   0.50 0.51 0.51 0.51
1.10 0.51 0.52 0.56 0.61   0.51 0.51 0.52 0.52
1.15 0.51 0.53 0.57 0.62   0.51 0.52 0.53 0.53
1.20 0.52 0.54 0.58 0.64   0.52 0.53 0.53 0.54
1.25 0.52 0.54 0.59 0.64   0.52 0.53 0.54 0.56
1.30 0.52 0.55 0.60 0.66   0.52 0.53 0.55 0.55
1.40 0.53 0.56 0.61 0.67   0.52 0.54 0.56 0.57
1.50 0.53 0.57 0.62 0.68   0.53 0.55 0.56 0.58