I know the normal distribution can represent many things in nature. Most items are normally distributed. I recently watched a video of a professor who claims that biomodal distributions provide evidence of cheating. He states that biomodal distribution "when external forces are applied to a data set that creates a systematic bias to a data set" aka cheating. He compares this information to previous grade distributions of students given the same test in other years when he gave the test and estimated that 1/3 of his students have cheated. My question is does a bimodal distribution really provide statistical evidence of cheating? Can't it be that some students do very poorly and some students do really well, leaving a peak that is low and a peak that is high? Do biomodal distribution really mean there is a higher probability of "when external forces are applied to a data set that creates a systematic bias to a data set?"
The link to the video is: https://www.youtube.com/watch?v=rbzJTTDO9f4
Yes, I get some students admitted to cheating, but that doesn't answer my question. My question is can a teacher really provide statistical evidence of someone cheating without them admitting it? I know statistics is all about probability, so can a teacher claim that the probability of this is really lower than a certain threshold and say because of this there exist a statistical significance of them cheating? And how can they approximate 1/3 of there students cheated just by comparing the bimodal distribution to a normal distribution.
To me, it seems that the teacher is just trying to use scare tactics with his "statistics" and guilt students into admitting to cheating rather than have any evidence of them cheating.
PS: I know cheating is wrong, but I know there must be a lot of innocent students in his class that were also accused of cheating, so that is why I asked this question. (I don't actually go to that university)
Best Answer
I could be mistaken, but I think that in general, whenever you see something that is too far against the norm, it raises red flags, which may be what he is talking about. Here is a glaring example from standardized testing, where the minimum score to pass this test was 30%:
Here is the original reddit post: https://www.reddit.com/r/dataisbeautiful/comments/27dx4q/distribution_of_results_of_the_matura_high_school/