[EMAIL PROTECTED] (Ben) wrote in news:[EMAIL PROTECTED]:
> Hi > I have a question for an upcoming test that I thought I might put to > anyone. > > If Jon and Ron both sat the same exam in different years say 200 and > 2001. Jon got 61 with a class average score of 60 and a standard > deviation of 5 and Ron got 57 where the average was 55 and the > standard deviation was 5. Who did better and why? > > I think that Ron did better as his score is further away from the > average score. Is this right? Is there a mathematical way to express > it? It really depends on what you mean by "did better." The definition you used is in fact quite commonly used, though I think it's rather nonsensical as it defines academic success in terms of triumph over others rather than comparison to some absolute standard (note that comparison, to, say, the long-term average score for everybody who ever took that exam would be a lot more defensible, IMHO, since it would be far less dependent on how well one's classmates did). OTOH, another definition of "did better" might be "based on what we know, what prediction can we make about the results we'd see if both Jon and Ron were to take a similar exam at the same time?" I think that's actually a more useful question to ask, since it's what you'd need to know if you had to choose between Jon and Ron, say for admission to an advanced program. Here I'd argue that Jon did better; while Ron was twice as far "ahead of the pack" than Jon, Jon's whole pack was 5 points ahead of Ron's, so Ron still winds up behind Jon. Another way to put it is that Ron was ahead of more students than Jon, but they weren't as good students as the ones Jon was up against. Of course, to do the latter comparison properly you need to have some notion of the "test/retest reliability" of the exam, which is how much the results would vary from test to test if the same person took a bunch of exams that all covered the same material. And we don't have that here. . . ================================================================= Instructions for joining and leaving this list, remarks about the problem of INAPPROPRIATE MESSAGES, and archives are available at: . http://jse.stat.ncsu.edu/ . =================================================================
