Executes the Van der Waerden version of non parametric tests (Normal scores tests)
Named for the Dutch mathematician Bartel Leendert van der Waerden, the Van der Waerden test is a statistical test that k population distribution functions are equal. The Van Der Waerden test converts the ranks to quantiles of the standard normal distribution. These are called normal scores and the test is computed from these normal scores. The standard ANOVA assumes that the errors (i.e., residuals) are normally distributed. If this normality assumption is not valid, an alternative is to use a non-parametric test. The advantage of the Van Der Waerden test is that it provides the high efficiency of the standard ANOVA analysis when the normality assumptions are in fact satisfied, but it also provides the robustness of the non-parametric test when the normality assumptions are not satisfied. This function compute the Normal Scores of 5 tests:
Levene, Mann-Whitney-Wilcoxon and Wilcoxon tests when there are 2 groups;
Kruskal-Wallis and Friedman test whene there are more than 2 groups.
The function will use a GUI to select the proper test. Moreover, the GUI will ask which version of Normal score do you want to use: Blom, Tukey, Rankit, Van der Waerden
Created by Giuseppe Cardillo
To cite this file, this would be an appropriate format: Cardillo G. (2010). NSCORES: Normal scores version of several non-parametric tests.
inputparser; code make up; github link
Blom, Tukey, Rankit, Van der Waerden Rank-Based Inverse Normal Transformations
multiple comparisons test added for Kruskal-Wallis and Friedman tests
change in help section for citation