Why does Cohens d suggest a large effect and Pearsons r suggest a negliglbe effect?
The difference between the result of Cohen’s d and the Pearson’s r for these data highlight the purpose of each test. Cohen’s d is designed to test the separation between group means whereas the Pearson product moment correlation coefficient, r, demonstrates the degree to which x varies as a factor of y. If we think about the data, we know that the pair-wise comparisons for each data point are actually comparing the scores of individual students from the treatment and control groups. The Pearson statistic compares Student 1, Treatment with Student 1, Control. Even if the effect of the intervention is considerable between the groups (Cohen’s d) it makes sense that the performance of Student 1, Treatment wouldn’t necessarily PREDICT the performance of Student 1, Control. For this reason, it is easy to see that you can’t really predict y from x in this case. Moreover, this example demonstrates the point that Pearson’s r is most appropriate for correlated data. Had we compared Student 1, T
