(1) After searching various sources, we found out that there are multiple ways used to calculate PS. Which is the commonly used method to calculate PS value corresponding to Cohen's d ? (2) Can the Cohen's d value which uses pooled standard deviation in its calculation, be estimated as a z score in the cumulative distribution table of standard normal distribution (i.e. z-table) .Is this procedure correct?
Hello Ranajay,
It depends. If both score distributions are normal in shape, and the variances are homogeneous, then the z-score approach works just fine regardless of which SD (pooled, or comparison group only) you use.
If the distributions are not normal in form, then it won't matter much what SD you use, the resulting estimate of % superiority will be wrong. An exact enumeration (like the classic definition of common-language effect size--of all possible A-B comparisons, the proportion of randomly selected cases in set A which exceed the value of randomly selected cases in set B) is the preferred method. Fancier definitions (Like Norman Cliff's dominance statistic, or Vargha & Delaney's A statistic) are available as well; no distributional assumptions required.
Good luck with your work.
You can check this link:
https://cran.r-project.org/web/packages/RProbSup/index.html
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