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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:

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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.

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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.

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  • Comments are not for extended discussion; this conversation has been moved to chat.
    – eykanal
    Mar 14, 2019 at 14:30

4 Answers 4

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First, as you already noted, the better scores and the bimodal distribution may have other reasons. For example:

  • One of three TAs for the course did an outstanding job.
  • The professor reused questions from previous exams (perhaps without noticing) and one third of the students informed themselves about previous tests.

Most importantly, the following thing is odd: It’s highly implausible that the rate of students who decide to cheat on their own increases by that amount from one year to the next. Thus, they would have to decide for cheating together or due to some common motivation. This in turn only makes sense if the cheating is a collaborative endeavour or if somebody is helping the cheaters.

Now, while such scenarios are not unthinkable, they are usually as likely as possible explanations that do not involve cheating (your mileage may vary depending on the circumstances). Moreover, even such a scenario happened, just repeating the exam is unlikely to solve it. Therefore the professor should first find out what actually happened.

So, the statistics may point at something being unusual, but without further investigations you cannot say that it’s cheating. Moreover, even if it is cheating, statistics can only tell you that it happened, put cannot point to any individual involved in it.

To address your individual questions:

  • Are professors allowed to accuse someone of cheating based on a general increase in test scores?

    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?

    Technically, yes. Almost everybody can accuse everybody else of everything as long as we are not entering the domain of libel laws. Will it be successful or a good idea? Probably not, at least in any reasonable university or jurisdiction. And that’s not even considering that he has not one but many students against him.

  • is it ethical and reasonable to assume that one third of the people in his class were cheating?

    Assuming something cannot be ethical or unethical; acting upon an assumption on the other hand may be, but that depends on the action.

  • Is it normal practice and ethical for professors to accuse someone of cheating just by looking at the student’s test scores?

    Normal practice – I never heard of it. Ethical – certainly not. There are several possible reasons for a good individual test result, e.g., hard work and plain luck. The professor should be aware of this and thus the accusation is unfounded and hence unethical.

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The OP aknowledged in the comments that the question was sparked by a specific incident, the Richard Quinn case in UCF 2010.

Viewing the video, Quinn had not just Statistics, but both physical evidence and witnesses: a student had left at his office door a "test bank" answered, and many students communicated that other students were bragging about how they had gotten hold of the test bank and so had all the answers prior to the exam.

Moreover, Quinn didn't just "accuse the class of cheating": he had already negotiated with the school "full immunity" to those that will admit to the deed... At least 200 students admitted the cheating after they were offered the equivalent of full immunity.

I don't know the man and I have nothing to do with Florida, or with the US education system for that matter. But based on the information I found, the Quinn case certainly does not qualify as an example characteristic of the answer asked by the OP.

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    Warning personal opinion: After rewatching the video, I don't consider it cheating, I consider it studying. I look up practice questions before I take a test all the time to see how well I am prepared for the test, I will take in class. The practice questions I do look up are almost never on the test, but they give me an understanding on what concepts I am strong at and which concepts I need to improve upon. But you are right, he did give them full immunity. He also mentioned to the students that didn't turn themselves in, they would be turned over to academic affairs and they may be expelled
    – James Smith
    Dec 20, 2015 at 20:59
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    @JamesSmith My answer was about the relevance of the Quinn case to your question. Your question is very general and could be asked, discussed and answered without any specific incident in mind. But since the specific incident was linked to your question, I felt it would contribute to the quality of this thread if I provided more specifics on it.
    – Alecos Papadopoulos
    Dec 20, 2015 at 21:07
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    @JamesSmith: Can the university expel you without other evidence just purely on statistics? – Note that in the UCF case there may be further evidence than the pure test score. For example, if only 35 of 50 multiple-choice questions came from the leaked bank, somebody who suceeded at all of those questions and those questions only has cheated beyond reasonable doubt. (That being said, I would not be surprised if they bluffed about having such information and granting immunity and redoing the exam was clever damage control.)
    – Wrzlprmft ♦
    Dec 20, 2015 at 21:15
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    In the UCF case, the professor obtained e-mail chains of involved cheaters and social media posts on people bragging that they cheated. He has a LOT more to go on than statistics.
    – Nelson
    Dec 21, 2015 at 0:33
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    In the UCF case, he had a ton of evidence....of good study habits of his students and his own incompetence/laziness at writing tests. Get as many practice questions as you can, and if you can get a copy of every question they've used or a test bank for your textbook, good for you. As a professor, this is why I never use test banks. I post all my past exams for my students to study from. I want them to practice on old exams and I write entirely new ones for each year. I hated the UCF case, because I felt the professor was an example of a terrible teacher taking out his flaws on his students.
    – JKreft
    Jul 29, 2018 at 12:55
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Statistical tests can indicate that there may be cheating. But, to accuse students, more proof is needed. Perhaps the statistics indicated that there may be a problem and closer investigation showed that someone got access to the exam beforehand (but, for investigation reasons the students were not told)?

In short, per se, statistics is not sufficient to prove anything, but it can direct attention to finding more compelling evidence (which you may not know about at this stage).

That being said, I have seen enough variations of this sort in capability of cohorts that to use just statistics as evidence for cheating is questionable practice.

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    +1. You say "Statistical tests can indicate that there is cheating.", But do these statistical tests shown indicate cheating? (Honest question, I'm not familiar with the statistics used to find anomalous results). Seems to me like changing from a bimodal distribution to a single modal distribution would not indicate (/hint at) cheating, but a fundamental change in the cohort. (E.g. the removal of this unit from one major). Can you tell more about the statistics that indicate cheating?
    – Frames Catherine White
    Dec 21, 2015 at 10:24
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    There are difficult, but popular topics where a bimodal distribution is quite typical. The good students pick them and the really weak ones pick them because they do not realise the difficulty. The middling students will avoid these topics, though, as they are often better than the weak ones to judge their own skills. Thus, the marks signature of a course may well be bimodal. In the R. Quinn case, below, it is the deviation from past distributions that raised the flags. Plus, Quinn claimed to have an informer. For a fun read, see the "cheating" chapter from the book "Freakonomics".
    – Captain Emacs
    Dec 21, 2015 at 13:05
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    "Statistical tests can indicate that there may be cheating". There, fixed that for you :-)
    – einpoklum
    Dec 21, 2015 at 23:40
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    I've TA'ed plenty of statistics courses. My experience is that the grades are almost always bimodal. I don't think this is because there is almost always cheating, but rather because it is almost always the case that some students study and some do not (especially in intro to stats).
    – Cliff AB
    Jun 7, 2016 at 23:06
  • We're talking about how to interpret stats about the course "intro to stats". How ironic. More to the point, this answer does not answer the question: Is it OK to accuse someone of cheating based on test scores? It's a long way (or, at least, it should be) from a mere accusation to expulsion. (Edit: The last sentence sort of answers the question: "... to use just statistics as evidence for cheating is questionable practice." But not clearly.)
    – Brian Drake
    Nov 23, 2020 at 1:09
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Punishing students without any concrete proof just because they are good on a test once is neither ethical, nor is it good teaching. Even if these students did cheat, they are shown clearly that it doesn't matter how they get good grades, they will be punished for getting good grades anyway. It will be very hard to find even a single teacher who won't get more evidence than statistics before punishing a student for cheating.

That said, statistics are what cause teachers to start looking for said evidence.

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  • It's not clear what your post adds over existing answers that seem to already address this point - for example, this answer. Can you edit your post to clarify what this adds?
    – ff524
    Dec 21, 2015 at 20:01
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    @ff524 The linked answer discusses the validity of using statistics as evidence, but dodges answering the actual question "Is it normal practice and ethical for professors to accuse someone of cheating just by looking at the student’s test scores?". This answer differs from the linked answer by specifying that such behavior is not ethical, and expands by explaining why accusing students without proof is bad teaching
    – Peter
    Dec 21, 2015 at 20:06

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