We have two sets of non-paired numbers, and we wanted to know if they were different, and if so, how different they were.

To that, we used Wilcoxon, which told us they were different (we got a significant p-value). To understand how different they were (the effect size), we used both Cliff's Delta and VDA. Both tell us that the difference has a small difference (cliffs=0.25440176, VDA=0.627200879790825).

Which one should I report? Is one better than the other?

  • $\begingroup$ Cliff's delta and VDA indicate "how different they were" in a certain sense. They don't measure the absolute difference in the values. That is, they don't indicate the difference in, say, the medians. Instead they are related to the probability that an observation in one group will be greater than an observation in the other group. $\endgroup$ – Sal Mangiafico May 10 '18 at 20:00
  • $\begingroup$ Cliff's delta is numerically equivalent to another effect size statistic called Freeman's theta. Freeman's theta can be used for more than two groups, and so can be used as an effect size for Kruskal-Wallis. $\endgroup$ – Sal Mangiafico May 10 '18 at 20:05

Cliff's d and VDA have a lineair relationship. Cliff's d ranges from -1 to 1 and VDA from 0 to 1. VDA = (Cliffs_d + 1)/2. So it does not matter which one you report, you can calculate one from the other. So that brings us to the question, which is better? Personally I like Cliff's d better, since it scales between -1 and 1, or when you take the absolute value, between 0 and 1, with 0 = no effect (overlapping data) and 1 strongest effect (no overlap between the data). Hope this helps. . . .

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  • $\begingroup$ VDA is calculated so that no effect results in a value of 0.50. A value of 1 indicated the complete stochastic superiority of group, and a value of 0 indicates the complete stochastic superiority of the other group. $\endgroup$ – Sal Mangiafico May 10 '18 at 20:10

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