Statistics work only if I have a reference point

[trinityvixen]

So I did poorly on a chemistry test this week. I'm not fussed about it for a number of reasons--I've done well on other tests, this is a course I'm not sure I need, I've already taken it so I'm not concerned about knowledge I don't have. What I am is confused. I figured I'd throw this out to the people I know who know stats better than I ever have, do, or will.

Our grades are computed based on "z-scores," as befits a curve (apparently) that takes into account the fact we can drop one grade. This score equals [my score]-[test average]/standard deviation. The average z-scores of the class are then ranked. This is all well and good, but what rank/score equals what grade is not specifically ever stated. They say they chart the z-score averages, presumably on a histogram, and wherever there is a "break" in the graph--meaning a significant drop in the numbers of people at a given average z-score--there will be a change in letter grade. But since you have no idea where those breaks will be until all the tests are counted, including the final...what the hell will your grade be?

This is a useless way of keeping track of how well I'm doing. Also, pardon me and my non-statistical thinking here, but how does grading people based on how much better/worse they are than their peers accurately value what they've learned? This is not a new problem I know--this is the curse of the curve--but still!

Comments

[kent-allard-jr.livejournal.com]

It's always hard to distinguish (a) things one doesn't understand from (b) things that don't make sense. This definitely sounds like (b).

Our grades are computed based on "z-scores," as befits a curve (apparently) that takes into account the fact we can drop one grade.

Does he mean that dropping one grade makes scores normally distributed? Because it's simply not true: I did the same in my classes, and the grades were never normal (they were strongly left-skewed).

They say they chart the z-score averages, presumably on a histogram, and wherever there is a "break" in the graph--meaning a significant drop in the numbers of people at a given average z-score--there will be a change in letter grade.

So lemme get this straight ... In Class I, half the students get -1s and the other half get +1s, so he'd hand out Bs to the first half, and As to the other. In Class II, a third get -1, a third get 0, and a third get +1s, so he'd give the first third Cs, the second Bs and the third As? That's nuts.

But since you have no idea where those breaks will be until all the tests are counted, including the final...what the hell will your grade be?

So here's what they do: They take your scores, divide them by 5, take the square root, convert to their natural log, add 16, multiply it by your social security number and then ... guess! Great fucking system they have there!

[kent-allard-jr.livejournal.com]

Does he mean that dropping one grade makes scores normally distributed?

In fact (on second thought) the exact opposite is true! Assume final grades are the average of several dice rolls. Their distribution would be bell shaped, and the more die rolls the closer to normal they'd be. Dropping the lowest die roll would make the distribution skew left, and would involve a smaller number of dice (thus making it less normal).

[ivy03.livejournal.com]

I suppose telling students that he'd drop their farthest outlying grade, up or down, to get a better normal distribution would probably lead to stabbing with pencils.

[trinityvixen.livejournal.com]

The grade with the lowest z-score is the one that's dropped, as it would, obviously, bring down your average the most. Don't know if that helps you at all.

[chuckro.livejournal.com]

They take your scores, divide them by 5, take the square root, convert to their natural log, add 16, multiply it by your social security number and then ... guess! Great fucking system they have there!

My department head, as his "contribution" to created a series of weighted scores, effectively had us multiply them by a random number and then normalize them back to percentiles. That is: He had us introduce rounding error.