How to scale grades to take into account how strong the students are? I am interested in different methods for scaling grades from a class test, say. In this case there is only one test and this gives the whole class grade. I remember from years ago a method that took into account the relative strength of the students taking the class by looking at their grades in other classes. However I can't remember the details at all.  The idea was that a hard test taken by strong students would be scaled up more than an easy test taken by weak students.

Is anyone familiar with this idea and how it might work mathematically?



In response to comments let me give an example. Say there is an optional class on Semiotics and Structuralism that the strongest students typically choose to take. The mean for this unit is 60% typically, say. Say there is also another optional class on how to spell the words in Harry Potter book one that the weakest students take. Say this gets the same mean of 60% typically.  It would be interesting to know what formulas have been used to scale the former class  so that the mean is higher than the latter.
are you asking about just converting everything into standardized scores? 

In which case, you take the mean of relative performance (for example, if you are teaching a senior level course, you might take the major gpa distribution rather than overall gpa distribution) assign everyone a z-score based on their position in the calculated normal distribution.

you do the same for your test, standardize the score. For example, if your test average is a 50 with an SD of 10, a person who got a 70 has a z of 2 while a 45 has a z of -.5. 

Now if you are planning on basing their recorded grade based on expected performance you are probably opening up a serious can of worms.  For example,  a student who consistently scores in the z score range of 1.8-2.1 and then only scores at a 1.5 is given an 75 (assuming mean 80 score, and 10 sd) while a student who consistently scores at a -.5 to -.8 range and scores a zero is given an 85 on the test.

If this is your plan, I would seriously rethink it. Not only will it upset students, it penalizes high performing students and rewards low performers.