Tristan Miller <[EMAIL PROTECTED]> wrote in message [EMAIL PROTECTED]">news:[EMAIL PROTECTED]... > 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. :)
To make the scaling, you have to either have the markers all mark some papers in common (or get some other estimate of the difference in ability, such as swapping which papers the markers do on some assignments), or make some drastic assumptions about student abilities (which are rarely equal across different groups, except in certain special circumstances). Assuming you *can* take average student abilities across classes as equal, then there are a variety of ways you might match mean and s.d., but the obvious one is the linear transformation you get by multiplying the B group's marks by the ratio of standard deviations (r = s_A/s_B, making the new sd equal to s_A), and then adding the difference d = x_A - r x_B. Glen . . ================================================================= Instructions for joining and leaving this list, remarks about the problem of INAPPROPRIATE MESSAGES, and archives are available at: . http://jse.stat.ncsu.edu/ . =================================================================
