There are at least two potential explanations for why students from group A get a statistically significantly higher average grade in the same course than those from group B. The first is discrimination against A in admissions: if members of A face a stricter ability cutoff to be accepted at the institution, then conditional on being accepted, they have higher average ability. One form of a stricter ability cutoff is requiring a higher score from members of A, provided admissions test scores are positively correlated with ability.
The second explanation is discrimination in favour of group A in grading: students from A are given better grades for the same work. To distinguish this from admissions discrimination against A, one way is to compare the relative grades of groups A and B across courses. If the difference in average grades is due to ability, then it should be quite stable across courses, compared to a difference coming from grading standards, which varies with each grader’s bias for A.
Of course, there is no clear line how much the relative grades of group A vary across courses under grading discrimination, as opposed to admissions bias. Only statistical conclusions can be drawn about the relative importance of the two opposing mechanisms driving the grade difference. The distinction is more difficult to make when there is a „cartel” in grading discrimination, so that all graders try to boost group A by the same amount, i.e. to minimise the variance in the advantage given to A. Conscious avoidance of detection could be one reason to reduce the dispersion in the relative grade improvement of A.
Another complication when trying to distinguish the causes of the grade difference is that ability may affect performance differentially across courses. An extreme case is if the same trait improves outcomes in one course, but worsens them in another, for example lateral thinking is beneficial in a creative course, but may harm performance when the main requirement is to follow rules and procedures. To better distinguish the types of discrimination, the variation in the group difference in average grades should be compared across similar courses. The ability-based explanation results in more similar grade differences between more closely related courses. Again, if graders in similar courses vary less in their bias than graders in unrelated fields, then distinguishing the types of discrimination is more difficult.