I am asking more of a theoretical question, I think. I'm doing some testing on two groups Group A (sample size 500) /Group B (sample Size 500) that are continuous ratio. They are both skewed distributions so I'm running a Wilcoxon Signed rank test. I'm getting significant results between the two (Z=26.928, pval=2.2e-16) and a large effect size (r= z/sqrt(N)=0.94).
Next I wanted to see whether I can predict Group A or B based on their data. I performed a logistic regression for this and found a 63% prediction rate for training (slightly lower for testing- 59%), which I am actually happy with because I do not want them to be predictable, but that's another story.
My question is if the groups are so different, why would the prediction be so low? I realize being different and being able to predict are two different things. I want to be sure my technique is Ok and if it is have some understanding as two why the groups could be so different, yet those differences cannot predict the group.