One choice of effect size for the Mann-Whitney U test is the common language effect size. For the Mann-Whitney U, this is the proportion of sample pairs that supports a stated hypothesis. More fundamental to the Wilcoxon-Mann-Whitney 2-sample test is the concordance probability, which is a pure measure of separation of the two groups.
The Mann-Whitney or Wilcoxon test compares two groups while the Kruskal-Wallis test compares 3. Just like in the ordinary ANOVA with three or more groups the procedure generally suggested is to do the overall ANOVA F test first and then look at pairwise comparisons in case there is a significant difference. I would do the same here with the
1. The Wilcoxon signed rank test actually does not require a degrees of freedom. In essence, the Wilcoxon signed rank test is evaluating whether or not the median of the differences is equal to 0, so this allows us to use the Central Limit Theorem and a z-score for the test statistic. Using the normal distribution gets rid of the need for a df.
You can use Mann-Whitney on the original data (with or without the zeros, depending on what makes sense). Just understand that it isn't a test of medians. It is a test of stochastic equality. That is, Ho is that the probablity of an observation in one group being higher than an observation in another group is 0.50.
Moreover, the Mann-Whitney U test, which is based on median, is the preferred test as prior research has also indicated that median is the preferred measurement for ordinal data. This is an important result as it establishes the Mann-Whitney U test as the most appropriate statistical test to be adopted for this study.
The other point is that Wilcoxon Mann-Whitney and related tests are not testing a hypothesis equivalent to OLS methods. ANOVA and regression compare means, while WMW methods calculate the
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what is wilcoxon mann whitney test