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It is common practice to share a histogram of grades with a class after a quiz or exam. However, my institute has very small classes. This year I have 6 students in my class, and in previous years I have had 3. It seems like showing the breakdown of grades (e.g. how many A's, B's, C's there were) in such a small class may be inappropriate, since students may easily be able to guess who got which grade. On the other hand, it seems only fair to tell students how they did relative to the rest of the class.

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    Why is it important that "it seems only fair to tell students how they did relative to the rest of the class"? How does this help anyone? – Buffy Dec 25 '19 at 12:06
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    I wonder if there is a standard "rule of thumb" number among statisticians for a minimum bin size that preserves individuals' privacy. Maybe a good question for Stats.SE. – Nate Eldredge Dec 25 '19 at 18:16
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    I don't know if it is relevant, because is not answering the question directly, but often grades distribution is usefull in order to know as a student how do you compare to others. To adress that in your situation you still can give them a mean and the standard deviation. – RomainL. Dec 26 '19 at 12:53
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    Please add a country tag, as the question is not even answerable without it. As is, all current answers are just speculation. I'm in Eastern Europe, and all grades are public and exam results are published on both the university website and physical bulletin boards. – Davor Dec 27 '19 at 12:29
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    At my university lecturers regularly release complete grade data with student id numbers and grades. The id numbers aren't exactly anonymous. Another reason why this question needs a location tag. – Nobody Dec 27 '19 at 15:40
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You probably want to check with your university policy on grade sharing so you don't wander into a problem with your local regulatory body.

As for my opinion:

I am from the US so the following examples are based on the Family Educational Rights and Privacy Act (FERPA), however they may be useful to you anyway.

Speaking from a STEM prospective, at my university in the very large auditorium classes, and even smaller (30-50 student) classes histograms were regularly either mentioned after the test or posted. It was very useful for a student to know, based on their grade, what percentile they fit into. For me, it helped me understand if I really understood the material or I was carried by a curve. Due to this I consider posting a distribution (anonymous) a highly useful tool for your students that actually care about their grade. In advanced classes where curves are common this could help them if they need to ask for more resources.

It's reasonable (albeit maybe not FERPA reasonable) to assume that as long as the grades are anonymous and the percentiles group into large enough bins students can't deduce other students exact grade which may be the loophole (discussed in the links below).

On the other hand you have small classes. Sharing a distribution of 10 students for example may give too much information to your students about other student's grades. Again, FERPA is the problem here. Is anonymous distribution of grades enough to protect you from an angry student? You may want to check your university teaching guide. If FERPA isn't an issue then it really comes down to if you think it will provide students some value. I can see it both ways. What information could the grade distribution of 3-6 students (for example) provide to the students? Not much I think.

There are some good points here posted by people on both sides. I don't personally see a problem with it (your case I lean more towards not doing it however) but FERPA is a headache and you are probably best not asking here, but rather asking your university.

There are some links on the web related to FERPA that may be similar to your local policy:

This link (non-edu) seems to imply the grade distribution falls outside the scope of grade disclosure rules.

This USC guide says grade posting is fine as long as student names are anonymized with a unique code and non-alphabetically listed.

CCCOnline seems to support posting grade distributions as being okay with FERPA.

ASU says something similar to the USC guide.

This UMSL link Says teachers are responsible for coming up with a way of distributing grades such that no student knows the other's grade.

EDIT

A comment has brought to my attention you may not be from the US. Unfortunately, I wasn't able to find a similar depth of resources compared to FERPA through Google and I have no experience with European law regarding grade distribution. I found the following AACRAO working group paper on the GDPR unfortunately it provides situations and questions but not answers. I apologize. As always, refer to your University for the final say on these matters.

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No, for exactly the reason you give. If just a couple students share their grades with each other, it becomes trivial for others to be discovered by process of elimination.

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    +1. Sometimes the short and obvious answer is the correct one. OP shouldn’t overthink this, in a class of 3-6 students grade ranking information would be statistically meaningless in any case. – Dan Romik Dec 25 '19 at 20:38
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    How are you answering with this kind of confidence without even knowing the region? This is absurd. – Davor Dec 27 '19 at 12:27
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    My multivariable calculus professor showed the grade distribution for a midterm exam where I got the lowest score. I don't understand what the point of that was. But now that I myself have taught multivariable calculus, I can tell my own students that I got the lowest grade in the class on a math test and I ended up OK. But I also don't show grade distributions for how my own students do because I don't see the point. Students generally do want to know the class average, though, so I do share that if they request it. – Grad student Dec 27 '19 at 16:53
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    @GradStudent Given how meaningless an average is for these kind of statistics, that seems rather pointless. Back in the day, grades were published on a piece of paper and hung up in the department. Personally I don't understand why I should care if other people knew my grades - it's university, not kindergarden after all. It was interesting to see how I did compared to the rest of the class to get an idea how hard the class was and if more effort was in order. – Voo Dec 28 '19 at 0:36
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    @Davor: agreed this answer is somewhat location-specific, and would be better if it acknowledged that — but at the same time, it’s clear from the question that the OP is in a place where individual students’ grades are not suposed to be made public, and so this answer is appropriate for the OP. – PLL Dec 28 '19 at 15:00
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Check if the university has a policy on this. This varies wildly across locations: in some places grades are still published with the students' names next to them; in others there are stated policies that this is not allowed. At my university, histograms are automatically published by the system no matter the number of students (even if 2), and there is no way to prevent this.

If there is no policy on this, it is your choice how much you want to weigh transparency vs data protection. There are also intermediate options, such as only publishing the mean, maximum and minimum grade, or the mean amd variance.

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    Indeed, at my university, the average grade, the average number of attempts necessary to pass, the number of passes and the number of signed-up can be read by anyone with the university login. Even if there was just one student. – Vladimir F Dec 27 '19 at 16:57
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I take issue with your premise:

It seems only fair to tell students how they did relative to the rest of the class

In a large class, this seems reasonable: if I know that I'm in the top 5%, I know that I am likely to get an A, regardless of my actual score. Even professors who "don't curve" usually adjust difficulty levels to achieve the desired outcome.

In a class with three students, this is not really the case -- giving three As or three Cs could be appropriate. Saying "you got the top score" doesn't really provide any information about my performance. So, I would argue that it provides no upside. Others have already covered the downside - namely, privacy violations.

I would suggest a better option would be to say: "Scores above 80 are A-range, 65 is B-range, 50 is C-range." This is both more useful to the student and sidesteps any privacy issue.

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  • Indeed, what I would say is "it seems only fair to tell the students how they should interpret their grade as a measure of how well they are meeting the learning objectives of the course". That's the information that is important to education (not relative placement). Telling students how they are doing relative to the rest of a large class was always a proxy for this anyway. – Greg Martin Dec 28 '19 at 16:44
  • Your point is valid, but students do want to know how they did relative to the rest of the class. Especially in a small class, if students feel they were the best student and got a B+ they may be satisfied knowing the class average was a C, but dismayed if the average was an A. – jerlich Jan 13 at 5:20
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I'm not sure how "common" it is to share a histogram, but I question the value of it. I also worry that it implies in some way that grading is competitive. The worst case, of course, is a zero-sum grading system in which to give person A a point, person B must be denied a point. That is evil. In fact, grading "on the curve" has this characteristic built in. Students are individuals and should be treated as individuals, not as statistics.

But, I wonder why you think it is desirable to post relative scores. What does that add to the educational process? Who does it benefit? Who does it discourage? If education is about "bragging rights" or "one-upmanship" then fine. But telling a student that they were worse than most of their peers is not, IMO, a way to encourage them to learn. Rather, it can lead to depression.

I suggest, instead, that grading be individual and that the philosophy is that everyone can earn top marks, as well as that everyone can fail.

Students need feedback, of course, but the feedback should be related to their own performance, not the performance of others. Education isn't a sporting event.

A histogram may be useful to the instructor, I think, but making it public, even in a large class, can be counterproductive.

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    One argument to defend histograms is transparency: students can know (and maybe complain) if an exam was "too hard" and no one got a good grade. More transparency incentivizes the instructor to design adequate exams. – wimi Dec 25 '19 at 15:38
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    @wimi, but it doesn't take student complaints to do such things. New instructors can/should be shepherded by more experienced colleagues to get it right. As I said, the histogram can be instructive for the instructor, as can guidelines from the institution. But the student "complaint" should be centered on their own mismatch between performance and grade. Not the grades of others. – Buffy Dec 25 '19 at 15:42
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    On the flip side, a student who feels their score is low may be reassured by knowing that many other students performed similarly. – Nate Eldredge Dec 25 '19 at 18:17
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    In my experience there is always some level of grading to the curve, if only implicitly. If a professor sets work that far too many students fail, the grades will be scaled up. – Anush Dec 26 '19 at 8:34
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    @Buffy of course, instructors and their "superiors" should strive to do things right. Transparency is there to make it harder for people who do not want to do things right... Anyway, I see from the answers/votes here that most people consider privacy more important, and maybe they are right. I just wanted to throw in a possible reply to all the questions you pose in your second paragraph ;) – wimi Dec 26 '19 at 19:08
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As much as the other answers are correct, there is an alternative solution if you indeed want to release the grade distributions without compromising on anonymity. You can use differential privacy (ε-differential privacy with a random response in this case seems applicable) to guarantee that no information can be gained regarding individuals grades, even if there is only one person in the class, while still ensuring statistical measures performed on the grades remain the same.

Differential privacy uses statistics to guarantee that anonymity is retained, by affording plausible deniability, while also ensuring statistical accuracy, and is widely used these days by companies wanting to make data releases (such as Google or Apple). The drawback of this is the grades you are releasing are only statistically accurate (to within a controlled threshold), but the individual grades themselves may or may not be correct.

I'd say in this case where the data has been thoroughly anonymized using these methods (as opposed to k-anonymity or l-diversity which have their drawbacks in small group sizes), then releasing this information poses no risk to individuals.

https://en.wikipedia.org/wiki/Differential_privacy

You can then take this one step further and release a distribution based on these anonymized grades, while still retaining the guarantee that individual grades cannot be obtained by any party.

It'd still be good to check academic policy, but in any case, this is a good measure to take if you want to protect your students.

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I give each student their grade individually - and don’t publish any “list” of any sort.

If the student then wants to “publish” their own grade then that is their prerogative.

This seems to satisfy the students and I don’t get any issues.

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    Depending on the region, publishing grades may even be mandatory. Anecdotes aren't that valuable. – Davor Dec 27 '19 at 12:32
  • @Davor so which region? Because what fits one won’t fit another. – Solar Mike Dec 27 '19 at 12:53
  • That's a question for OP. Any answer given before OP specifies a region is useless. – Davor Dec 27 '19 at 14:34
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If you don't want to disclose to the students the results of others, but you want to let the students know how they did compared to others, you could individually disclose their percentile.

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    This still allows students to deduce something about their classmates' scores, especially in a small class. Take 3 students as in OP's example. If Student A gets a score of 85 and is told they are at the 100th percentile, they know both of their classmates got less than 85. If Student B gets a score of 70 and is told they are at the 66th percentile, they know one of their classmates scored above 70 and the other scored below, and they can probably guess which is which. – Nate Eldredge Dec 25 '19 at 18:15
  • Yeah, that is fair point, in class of 3 this is not going to work that well. – sjaustirni Dec 26 '19 at 16:18
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The 'transaction' you and your students are engaged in is between you [the university] and themselves [the student]. If you are secure that your assessment was adequate and fair, there is nothing to be gained in comparing students against each other, especially publicly. If you are not secure in your testing methodology, you might consider grading on a curve, which by definition compares individuals against each other, but again, this need not be a public exercise.

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