CDF of the student performance for a given PI.
Correlation: Correlation between PI and the performance in class is -0.60.
Risk and Odds ratio: For students with high PI (PI>.9) vs. students with low PI (PI < .1). The Risk Ratio of this population 59. That means students are 59 times more likely to fail. The Odds Ratio of this population 166. The odds of their failure are 160 times more than the other group. The Population Log Odds Ratio of this population with standard error = 5.110 +/- 0.088. The Cliff's Delta for these two groups is 0.86 which is close to the maximum possible value of 1! This essentially says that there is no overlap between the two distributions. The difference in medians is 66 (93 vs. 27) and the difference in means of the two populations is 54 (90 vs. 36). When students with medium PI (.45<PI<.55) are compared with low PI , the risk ratio is 15 and the odds ratio is 32.
(Cliff (1993) interprets that this is a measure of dominance, a concept that refers to the degree of overlap between two distributions. All possible values of Cliff's Deltameasures are in the closed interval [-1, +1].)