Field | rate | f. applicants | f. accepted | m. applicants | m. accepted |
Education | 10 | 1000 | 100 | 100 | 10 |
Social Sciences | 20 | 500 | 100 | 300 | 60 |
Engineering | 30 | 200 | 60 | 1300 | 390 |
total | 1700 | 260 | 1700 | 460 |
If we look at the aggregated total distribution the selection of students seems biased. Many more male students (460) are accepted than female (260). The reason is that female students applied more for fields with lower acceptance rate (higher competition). But this information is not shown anymore in the total (projected) distribution, parts (marginals, projections) do not in general determine wholes (overall distributions). A similar example with patients in a hospital can be found in Glymour et. al. [11, pg. 20].