Let's assume, for a moment, that you believe the average and stdev of performance for groups of students are the same. Each group is defined as "those students graded by a single grader."
then you can rescale each group as follows. For grader A, all grades in the group are scaled using: grade' (grade prime) = (raw grade - mean_of_A_grp)/stdev_A and so forth for group B, C, etc. Then with all the grades together, decide what the overall average, mean_overall, and stdev, stdev_overall, you would like them to have, and rescale again: reported grade = grade' * stdev_overall + mean_overall this will work if you assert loudly that all subgroups are drawn from t he same population (the average & stdev depends only on the grader, not the students), and if your grading scale is truly linear. A scale with a maximum of 100% ain't linear at the top end, sorry. I would be more concerned that the graders can interpret the answers in such blatantly different ways. Perhaps the students do the same, which begs the question of the precision & usefulness of the questions. Reviewing the questions with your graders might tighten up your (instructor's) part of the process. Jay Tristan Miller wrote: > > Greetings. > > It is sometimes the case that, when a large group of assignments are > graded by different markers, one marker will grade much more or less > harshly than the others. So that students graded by said marker are not > unfairly (dis)advantaged, it is the policy in some places to scale those > marks up or down. > > My questions, then, are as follows: > > 1) Given that the n ideally-marked assignments (sample A) have mean grade > x_A and standard deviation s_A, is there some function f() which can be > applied indiscriminately to the m poorly-marked assignments (sample B) > with mean grade x_B and standard deviation s_B, such that their mean and > standard deviation are changed to x_A and s_A, respectively? > > 2) Is f() unique? Are there multiple such f()s? An infinity of them? > > 3) If f() is not linear, does it have a linear approximation? > > 4) Is such a scaling even desirable? It seems to me that, assuming a > scaling is mandated, bringing the mean and standard deviation into line > with the other assignments is the fairest possible way of adjusting the > marks. But then again, this is just a gut feeling of mine and I haven't > gone through a rigorous proof. I get the feeling that this question has > already been asked and that the results and discussion are published > somewhere. :) > > -- > \\\ Tristan Miller > \\\ Department of Computer Science, University of Toronto > \\\ http://www.cs.toronto.edu/~psy/ > > . > . > ================================================================= > Instructions for joining and leaving this list, remarks about the > problem of INAPPROPRIATE MESSAGES, and archives are available at: > . http://jse.stat.ncsu.edu/ . > ================================================================= -- Jay Warner Principal Scientist Warner Consulting, Inc. 4444 North Green Bay Road Racine, WI 53404-1216 USA Ph: (262) 634-9100 FAX: (262) 681-1133 email: [EMAIL PROTECTED] web: http://www.a2q.com The A2Q Method (tm) -- What do you want to improve today? . . ================================================================= Instructions for joining and leaving this list, remarks about the problem of INAPPROPRIATE MESSAGES, and archives are available at: . http://jse.stat.ncsu.edu/ . =================================================================
