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Problem: A college looks at the grade point average (GPA) of its full-time and part-time students. Grades in science courses are generally lower than grades in other courses. There are few science majors among part-time students but many science majors among full-time students. The college finds that full-time students who are science majors have higher GPAs than part-time students who are science majors. Full-time students who are not science majors also have higher GPAs than part-time students who are not science majors. Yet part-time students as a group have higher GPAs than full-time students. This finding is
Required:
(i) not possible: if both science and other majors who are full-time have higher GPAs than those who are part-time, then all full-time students together must have higher GPAs than all part-time students together.
(ii) an example of Simpson's paradox: full-time students do better in both kinds of courses but worse overall because they take more science courses.
(iii) due to comparing two conditional distributions that should not be compared.
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