Two students who were hoping to be accepted into graduate school were discussing the results of their graduate entrance examination. Joe had taken the exam in January and had scored very poorly. He placed at the 30th percentile. He re-took the exam in June and did much better. His score improved to the 45th percentile. Mary had scored at the 79th percentile. Joe was trying to persuade Mary to re-take the exam because her grade would probably go up as his had. Assuming that practice effects are not an issue, would you agree with Joe's theory? What statistical explanation would you give to explain Joe's improvement in score?
What will be an ideal response?
Correct Answer:
Statistical regression would predict that Joe, who scored well below the mean on the first test, would score closer to the mean on the second. Mary's score, on the other hand, would be expected be lower the second time.
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