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The effect size of those tests are calculated as follows: Kruskal-Wallis and Friedman tests give you a chi-squared.However, its degree of freedom is more than 1, and thus it is not straightforward to convert the chi-squared into the effect size.
This means that you can compare the data only across one factor and unfortunately, you cannot easily extend these tests to two-way or mixed-design as we can do with ANOVA.As we do multiple t tests with Bonferroni or Holm correction, we can do Mann-Whitney or Wilcoxon tests with the same corrections.If you have unpaired (factorial, or non-repeated-measure) data, you can do pairwise comparison with a Mann-Whitney test.For doing this, see the Mann-Whitney test or the Wilcoxon test.Instead of Bonferroni correction, you can also use Holm correction.Thus, we calculate the effect size for the post-hoc comparison.
Similar to ANOVA, you need to do a post-hoc test after Kruskal-Wallis and Friedman if you find a significant effect.
Unfortunately, there is no straight way to calculate the effect size of Kruskal Wallis test or Friedman test.
Instead, you can calculate the effect size in the post-hoc test with Mann-Whitney or Wilcoxon test.
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