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.

[linaerys.livejournal.com]

I think a curve only works/is necessary if the test is much harder than it should be. I took a Computer Science class in college, and on the first test, the average was 15%. People who got 30% got an A. The professor apologized for making such a hard test.

Of course, as the person who got 95%, I was pretty annoyed, but honestly, that is the fair way. He shouldn't fail the entire class if he wasn't able to teach or write a test that accurately reflected his teaching.

[ivy03.livejournal.com]

I once got an orgo test back with an enormous note on the front that said DON'T PANIC!!!!! and then explained the curve and only after you flipped that aside did you see your number grade.

I, like you, had a fine number even without the curve, but I suppose wanting an A-er A is a bit obnoxious. :)

[trinityvixen.livejournal.com]

I had that sorta happen once. Nowhere near as high as you, but the average on a physics test in college was in the low 30s, and I scored in the high 50s/low 60s. I was the kid ruining the curve on that one.

[linaerys.livejournal.com]

I had a really good high school computer science teacher and most of the kids in the class had never done computer science before.

Your grading system sound really hard to understand.

[trinityvixen.livejournal.com]

I was the same way! I had a phenomenal physics teacher in high school--he was so good, I never had to study for standardized tests and I aced them. I was teaching my friends who had the I-have-tenure-and-will-retire-next-year guy. A lot of people in college physics were lost because they were coming into a hard subject with no background. Just a little bit of foreknowledge is a great thing.

I do not, even after reading all the explanations thus far offered, understand it still. I mean, I read the explanation they gave us. I see the scores go into the stats machine, but I cannot understand how they will come out. I get that they probably have a lot of people pissed off and demanding grade reviews (this is a course I'm betting is lousy with pre-meds). But there has to be a better way.

[ivy03.livejournal.com]

That's how grades were done in the chemistry department. I know for certain it was how honors were determined. (Curse Hannah and her outlierness! Making suma unreachable for the rest of us!)

But if you think about what a grade is supposed to be, that is, a way of sorting people into categories of how well they've done, then this is the most logical way to do it. You make the grades break where the clusters break, so you aren't punishing people or rewarding them for being one point over or below an arbitrary pre-set line. If the point of grades are to group students into groups relative to each other, this method makes sense.

If the point of a grade is to rate a student against an outside benchmark irrespective of how other people are doing, then obviously this doesn't make sense.

But you know, I majored in a department with the lowest average GPA at Princeton. I was told in one class that only one student would be receiving an A. So my experience is not really a reassuring one with respect to grades.

[ivy03.livejournal.com]

I should revise this to say--I don't know about z-scores, it's the histogram way of grouping people by natural breaks that I'm referring to.

[chuckro.livejournal.com]

The only real value to a curve is offsetting the professor's inability to teach/write a good test. Grades are only useful as a relative score (you versus other students) if they were first an absolute score (how much of the material you know) which means that the only thing grade deflation does is hurt students when they are then compared again other departments and schools.

If they really wanted to make grades useflu as an arbitrary measure, they'd need to give both an "absolute" score of how much of the subject you knew, based an a standardized exam, and a "relative" score versus your class and previous classes by the same professor. But that would be much harder to turn into a GPA that idiot recruiters could put in a spreadsheet and sort by.

[trinityvixen.livejournal.com]

I think you've got a pretty fair system. This is an intro course; the material is probably fixed and the teachers rotate. It should be pretty easy to generate a standardized score and then apply it against the scores in class.

Man, whatever happened to just "If you score this, it is an A"? I knew where I was with that scale.

[xannoside.livejournal.com]

Reasons to grade on a curve:

1) Assigning grades based on the 100-pt scale divided by the # of questions is not reflective of student ability.
2) The school administration wants less Cs and Ds.

This just sounds like pretending to be awesome at stats.

Plus, if you have 40 people or less, you won't have a normal curve. And if they have less than 100, they should be using T-scores, not Z-scores, anyways.

[mithras03.livejournal.com]

This sort of thing really freaked out the American students at LSE, where the highest number grade you can really ever get is a 70. And everything is on a "Distinction," "Merit," "Pass," scale, so... no actual grades. What do I do without the alphabet validation!?!?!?!

[trinityvixen.livejournal.com]

It's an intro course, so they have well over 100 students.

[xannoside.livejournal.com]

Ah, so they're part of the "lies, damn lies, and statistics" side of things. :P

[trinityvixen.livejournal.com]

Bingo. Although, I'm not sure that the "lies" are separate from the stats in this case.