ROBUSTNESS AND POWER OF THE T, PERMUTATION T AND WILCOXON TESTS

Data analysis is conducted via parametric or §nonparametric methods, depending on the data. §Authors state that parametric techniques §are more robust with regard to Type I error and more §powerful than nonparametric techniques. §Nonparametric methods are good alternatives to §parametric methods being robust and powerful under §non-normality. §Permutation tests offer advantages compared to §parametric tests as they require fewer §assumptions. It was found that they are robust with §regard to Type I error and powerful. However, §permutation tests maintain the Type I error to the §nominal with no evidence that they are more §powerful than nonparametric tests.§Monte Carlo simulations were used to investigate the §Type I error and power of the t-, permutation t- and §the Wilcoxon tests for some distributions.It §was found that, under normality, the t and §permutation t-tests were robust with regard to Type §I error compared to the Wilcoxon test. They were §also slightly more powerful than the Wilcoxon test. §However under non-normality, the Wilcoxon test was §robust with regard to Type I error and much more §powerful than the t and permutation t-tests.