Effect size for Wilconxon signed-rank test
I am running a non-parametric paired samples analysis.
I've been reading about calculation of the effect size r for this analysis and most literature referes to the formula proposed by Rosenthal (1991). The formula is: r = Z/sqrt(N). In the case of JASP, the way the same coefficient r is computed seems to be quite different: W / ((n*(n+1))/2) * 2 - 1 (thank you Johnny van Doorn for the clarification).
If we assume N as the number of subjects (e.g., 10 subjects evaluated in two moments), the calculation of this effect size is (in my example) varies from r=.693 to r=.782, depending on whether the calculation is based on the Rosenthal formula or as it is implemented in JASP.
To add even more noise to this, Field (2009) and Pallant (2007) propose that when dealing with related samples, N should refer to the number of observations (i.e., 10x2 in my example) and thus this difference is even more pronounced (r=.490). I am reporting such analysis in a revision of a manuscript and I would like to have more certainty in how I should compute this ES, given the impact that this has for the magnitude of the effect.
Do you have any thought on the most accepted way of computing this?
Thank you very much for your attention