Non parametric tests based on ranks
As previously mentioned, parametric tests are not robust because of their heavy reliance on the normality assumption. Some classical parametric tests have non parametric counterparts based on ranks.
Several non parametric tests exist including permutation test, rank (Wilcoxon) test and bootstrap. Using bootstrap method, you have additional benefit. You can even go one step further beyond the estimation of sampling distribution.
 See also: Distribution, Variance, Normal distribution, ANOVA, Regression
  
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