Statistics effects size rosenthal

Question

Hello. I am curious about the effect size, Rosenthal’s r. I understand it shows the strength of an effect. I am confused about its relationship with persons r. For example if I am comparing treatment between day 0 to day 30 to a no treatment condition. What things is the linear relationship between? That is, what would be on the x and y? I am trying to understand how it would look charted and why it’s related to Pearson. It seems there would be no relationship between control and treatment. Or is number of days on one axis?

Answer 1

The pearson correlation is related to the difference between two groups as measured by Cohen's d. Graphically, the smaller the difference the more tge shared variance. Shared variance implies correlation. Rosenthal's r is the non parametric analog. A Wilcoxin non par paired t produces a z statistic which can be converted to Rosenthal's r.