On p. 12 of Fritz Morris, Richler (2011) in their article Effect Size Estimates: Current Use, Calculations, and Interpretation, they say, "The z value can be used to calculate an effect size, such as the r proposed by Cohen (1988); Cohen’s guidelines for r are that a large effect is .5, a medium effect is .3, and a small effect is .1 (Coolican, 2009, p. 395)." Shouldn't r be squared to determine the effect size with nonparametric data? Does anyone have a source to verify or refute this sentence?
The article can be found in the Journal of Experimental Psychology: General.
“A Call for Greater Use of Nonparametric Statistics,” pages 13-15. The authors (Leech & Onwuegbuzie) Grissom and Kim (2012) have some effect size estimators for nonparametric statistics. For the two-group independent samples design, the Mann-Whitney U statistic and then divide it by the product of the two sample sizes. That is, the probability that a score randomly drawn from population a will be greater than a score randomly drawn from population b. here you have a web calculator for your need. Non-parametric need Mann-Whitney or Wilcoxon
https://www.psychometrica.de/effect_size.html
Thank you very much, Beatrice, a very interesting page with information that I did not know. In journals today they ask for the omega squared instead of the eta squared that appears in the page that you mentioned, Beatrice. The eta squared reports the size of the differences in the sample and the omega in the population. I find it hard to believe that those responsible for SPSS continue to simply use the partial eta square and do not include other estimators. The same is true for factorial analysis and internal consistency, SPSS only provides outdated methods. Do you know if there are any pages that offer syntax for these estimators in SPSS?
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