Wikipedia defines 'grading on a curve' as a

a statistical method of assigning grades designed to yield a pre-determined distribution of grades among the students in a class.

The article does not say much about when it's appropriate/inappropriate to grade on a curve, but it does state

The ultimate objective of grading curves is to minimize or eliminate the influence of variation between different instructors of the same course

I take it then that if a course has only one instructor then that would remove an argument for grading on a curve. It also seems to me that it might be inappropriate to grade on a curve when a course cohort is extremely small, since it would then be hard to say what grades 'should' be given.

What other factors make grading on a curve more/less appropriate? Are there factors that make it absolutely inappropriate?

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    $\begingroup$ Note that it is rare for a course to have only one instructor, unless it is run only once and never repeated by anybody. Even a course that is taught twice (at different times) by the same person has to be considered as having two "instructors"--that is, it consists of two different groups of students to be graded. Regardless, there are interesting statistical questions here that we can focus on. $\endgroup$ – whuber Jun 25 '15 at 16:23
  • $\begingroup$ I don't like it. Performance is too much based on how others do and not how well you know the material. In one class you could get a C and another an A for knowing the exact same amount of material. $\endgroup$ – Glen Jun 25 '15 at 18:12

I grade on a curve because I want a grade that is relative to the performance of all of the students in that class. If the test is too difficult for any students to get 90% or higher, absolute grades are not appropriate and a curve should be used. I design the test such that it is nearly impossible for anyone to get 100%. I design it that way to produce a score that tells the difference between the stronger and weaker students. Therefore, I grade against the average of scores, and use standard deviations to delineate letter grades.

Another issue would be the life threatening nature of the subject matter. I would think a driver's license test should have an absolute grade, because if you do not know what a stop sign is, people die. The purpose here is to test to a "hurdle rate", a minimum set of required information the student must know, not to differentiate between good and bad drivers.

Similar situation for engineering classes when designing bridges, cars, planes, etc. You must design the bridge right or people could die. These classes have an absolute grading scale. There is also no partial credit. You either built the bridge right or you didn't, getting the general idea right doesn't work.

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    $\begingroup$ I think, even if more indirectly, that such an argument could be made in any field. What about an economist designing inefficient policies, causing people to die because the country is less wealthy than it could be with better policies, meaning that it is, e.g., not capable of paying as much on healthcare? Maybe my view on this explains why I do not think grading to the curve is a good idea. $\endgroup$ – Christoph Hanck Jun 25 '15 at 18:09
  • $\begingroup$ Statistically speaking, you are using a grading strategy that lays firmly on the variance side of the bias-variance tradeoff. You are assuming that each of your classes is a representative sample of the people who would take your course and who would also use their course evaluation as a way to signal their level of mastery of a topic. I think it would be much better to design a curve based on a larger sample of students...possibly of all students who took the class using the same or similar curriculum. $\endgroup$ – Brash Equilibrium Jun 25 '15 at 22:57

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