# Effect size for Wilcoxon Rank Sum test

I'm unsure how to calculate the effect size after applying a Wilcoxon rank-sum test. I'm using scipy.stats.ranksums, where the outputs are z, p. Looking at the implementation of the test, it seems z is assumed to be normally distributed - could I just calculate Cohen's d as discussed here?

I'm confused since Wikipedia offers alternative effect sizes for these non-parametric tests, but then also, the article states that the Wilcoxon rank-sum and the Mann-Whitney-U tests are the same, while scipy clearly implements them quite differently. Unfortunately, I cannot apply the MWU test since some of my comparisons involve samples with zero variance which leads to errors with MWU but not rank-sums.

• You can't assume that a constant column is has a sum of ranks that is normally distributed. Indeed scipy.stats.ranksums doesn't handle ties. Did you read the documentation for these functions? It's quite clearly stated. – Glen_b Aug 11 '16 at 8:29
• Depending on your needs, you can show Kendall's rank correlation between the binary grouping variable and your numeric column. A test on this correlation will provide similar p value than the rank sum test. – Michael M Aug 11 '16 at 8:35