Let’s say a professor has seen that the average score for the midterm exam was a grade and a half higher than it was in previous years. Because of this he gained a reasonable suspicion of cheating (he has been teaching the course for several years in the same way and this is the first time he has received such high scores). He looked at the score distributions and found it to be bimodal:
He went on to assume that, since this distribution wasn’t like his normal distribution he had received on his test scores in previous years, one third of all his students cheated on the mid-term.
Now here comes the question, is it ethical and reasonable to assume that one third of the people in his class were cheating? Maybe the distributions were different and bimodial because some students studied harder (causing peak at better scores), while others didn’t (peak at lower scores). Are professors allowed to make everyone retake the test because of this data (even the ones who took it honestly). This punishment seems like he is punishing the supposed two thirds of the class that took it honestly.
The professor goes on to claim that those students who had significantly higher scores than in their previous test must have cheated! Are professors allowed to that? What if they got a bad score on the previous test because they didn’t study and they got a good score on the mid-term because they did study? Also what if a student has a good score on the previous test and the mid-term because he cheated on both? Or what if the student was honest and received a good score on both test because he is a hard working student? So my question, Is it normal practice and ethical for professors to accuse someone of cheating just by looking at the student’s test scores?
PS: This didn't happen to me. I just heard about it from a friend.