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July 31st, 2017, 07:46 PM   #1
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Grading on a Curve

This question involves potential ways to curve a quiz grade as well as the overall question, should I? I'm interested in your input.

The background info: I teach a graduate level class on partnership taxation. My students have disappointed me this semester a little bit... On the most recent quiz, the average score was a 69.7%. One person aced the quiz.

These are open book quizzes that are not timed where the students can save the quiz and return to it, ask me questions if they aren't understanding any of the material, etc. They have every opportunity in the world to ace them. I only included questions addressed by the text, but in upcoming courses they won't receive that luxury as at this level they are supposed to be able to look up the Tax Code and Federal Regulations for answers too if not court cases and other guidance. Further, I quiz on general principles for the most part as opposed to really making them dig for specifics. I hope you can understand my reluctance when it comes to giving them a free boost in their grades.

Each question was worth between 2 and 4 points with a total possible of 25 points. Of the 8 questions on the quiz, the average success rate (percentage) was:

Q1, 3 pts: 71.43
Q2, 2 pts: 78.58
Q3, 3 pts: 85.72
Q4, 4 pts: 92.86
Q5, 3 pts: 92.86
Q6, 4 pts: 14.29 (comprehensive, more difficult question)
Q7, 3 Pts: 78.58
Q8, 3 Pts: 57.15 (oddly enough, not a difficult question I'd expect undergrads to get)


Here are the descriptive stats out of Excel with respect to their overall grades:

Mean 17.42857143
Standard Error 1.333071665
Median 18
Mode 21
Standard Deviation 4.987897441
Sample Variance 24.87912088
Kurtosis 0.089678713
Skewness -0.765811252
Range 18
Minimum 7
Maximum 25
Sum 244
Count 14
Confidence Level(95.0%) 2.879926241


Here are the students' overall scores out of 25:

16
21
25
12
18
21
18
21
15
21
7
21
10
18


With one person having aced the quiz, I'm not sure how to incorporate any curve...

Any suggestions?

Last edited by AplanisTophet; July 31st, 2017 at 07:56 PM.
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August 1st, 2017, 04:16 AM   #2
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One has to wonder whether those who didn't get even half of the available points were just guessing their answers, especially the student who got only 7 points.
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August 1st, 2017, 04:34 AM   #3
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This is just one quiz? What is its overall weighting for the unit? I don't see why you would need to boost them at all.. Especially if it is open book without time limit etc. as you have stated.

Last edited by skipjack; August 1st, 2017 at 05:46 AM.
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August 1st, 2017, 03:44 PM   #4
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Quote:
Originally Posted by skipjack View Post
One has to wonder whether those who didn't get even half of the available points were just guessing their answers, especially the student who got only 7 points.
Do we know if the questions are multiple choice? There were 106 out of 350 points not earned. If the questions had 4 choices and all the wrong answers came from random guessing where the points not earned should be about 3 times the amount of points earned from correct guesses. 106/3 = 35 when rounded to the nearest whole number. This would mean 209/350 = 59.7% of points that were earned without random guessing. Of course sometimes students eliminate some choices and then guess, and some wrong answers are by students who were confident they were right rather than guesses.

Hofstra Law School require course grades to be curved with a mean of about 3. The grade distributions must be close to:

A or A+: 8%
A-: 14%
B+: 26%
B: 19%
B-: 13%
C+: 7%
C: 6%
C-: 5%
D+ or D: 2%
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August 1st, 2017, 04:05 PM   #5
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I had a very good friend who was an adjunct professor at a law school. He got let ago for not grading second and third year students generously enough. (He was a hard ass: he had put himself through law school working at a blast furnace in a steel mill at night.) So I get your plight.

Here are my thoughts.

Grade this quiz straight for now. See how the students do overall by end of term. If you still want to make adjustments then, come back with the stats and ask for advice. At this point, I'd be giving incentives for people to pay attention.

I've worked with tax accountants and tax attorneys quite a bit. You give rotten advice, and clients are not happy, and bad things can happen to the firm.
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August 1st, 2017, 06:34 PM   #6
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Quote:
Originally Posted by skipjack View Post
One has to wonder whether those who didn't get even half of the available points were just guessing their answers, especially the student who got only 7 points.
I spent an hour working 1-on-1 with that student today. The student claims she read the text and listened to the lectures but still managed to struggle. We went through each quiz question and it was clear she didn't really know the material. Nevertheless, she was one of students that got the difficult comprehensive question correct. It turns out that was a lucky guess because she had no idea how to approach the question when we went over it. Her actual score would have been a 3 out of 25...

I am sure that some other students were guessing at some point too. I try to make each potential answer seem plausible, so on some questions ruling out a couple of choices is not really possible unless you know the material. There are quite a few aspects of partnership taxation that are not obvious.
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August 1st, 2017, 06:53 PM   #7
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Quote:
Originally Posted by EvanJ View Post
Do we know if the questions are multiple choice? There were 106 out of 350 points not earned. If the questions had 4 choices and all the wrong answers came from random guessing where the points not earned should be about 3 times the amount of points earned from correct guesses. 106/3 = 35 when rounded to the nearest whole number. This would mean 209/350 = 59.7% of points that were earned without random guessing. Of course sometimes students eliminate some choices and then guess, and some wrong answers are by students who were confident they were right rather than guesses.

Hofstra Law School require course grades to be curved with a mean of about 3. The grade distributions must be close to:

A or A+: 8%
A-: 14%
B+: 26%
B: 19%
B-: 13%
C+: 7%
C: 6%
C-: 5%
D+ or D: 2%
I don't have a similar requirement, but I nevertheless would like to see my students performing along those lines if not better because they all truly know the material. Obviously, not every student is going to earn an A. If they don't in my class, however, it will have a lot to do with effort as opposed to just ability.

The material itself isn't rocket science, but we do have a lot to cover. What is difficult for these students is if I pose questions that they have to research an answer for. They are still developing their ability to research despite the expectation that they are able to at least look up and cite the Code and Regulations. That is why I generally quiz on principles instead of having them dig for specifics at this point. Everything is addressed by the text in some form when it comes to the quizzes, whereas in their discussions and papers I require proper citations and reward them more for researching.
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August 1st, 2017, 07:10 PM   #8
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Quote:
Originally Posted by JeffM1 View Post
I had a very good friend who was an adjunct professor at a law school. He got let ago for not grading second and third year students generously enough. (He was a hard ass: he had put himself through law school working at a blast furnace in a steel mill at night.) So I get your plight.

Here are my thoughts.

Grade this quiz straight for now. See how the students do overall by end of term. If you still want to make adjustments then, come back with the stats and ask for advice. At this point, I'd be giving incentives for people to pay attention.

I've worked with tax accountants and tax attorneys quite a bit. You give rotten advice, and clients are not happy, and bad things can happen to the firm.
I like your thoughts. The students have plenty of room on their papers and discussions to improve their grades.

You're quite right in that, when we screw up, people sometimes can really be hurt by it. Thankfully we're not surgeons in that regard, but still, it hurts with respect to peoples' pocketbooks and also in terms of stress and time lost.

I recently published a paper in TAXPRO Journal where I advocated for regulating paid tax preparers. To quote myself, when it comes to your average chain outlet, "preparers only correctly prepare [relatively simple returns free of legal ambiguity] somewhere between 19.68% and 37.19% of the time." That stat is computed with 95% confidence using the conventional formula for an interval estimate of a population proportion given the limited sample I had to work with of 102 tested returns. Still, that's really bleak. Tax pros certainly are not all created equal and their services are not a commodity.

To that end, I want to be a bit of a hard ass but I'm really not. On the quizzes, my hands are tied because their score is what it is absent a curve. On their papers and discussions there is more room for subjective grading.

You know what the scary part of this is though?... Most of my students are themselves seasoned tax professionals. When I went through the Masters program, I had already been working for about a decade. I got a 4.0 and often times 100% throughout entire courses because I didn't need to relearn it. I already knew it. That's what I'd expect from anyone holding themselves out as a tax professional.

Anyways, sorry for the bit of a rant, but one more question please. Assuming I did want to curve a quiz like this, how would you suggest I go about doing it based solely on the information in the OP?
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August 2nd, 2017, 12:26 AM   #9
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Grade Points
$\ \ \ $ A $\ \ $ 22-25
$\ \ \ $ B $\ \ $ 18-21
$\ \ \ $ C $\ \ $ 14-17
$\ \ \ $ D $\ \ $ 10-13
$\ \ \ $ E $\ \ \ \ $ 6-9

Ideally, D and E grades should be treated as unsatisfactory.
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August 2nd, 2017, 05:33 PM   #10
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Quote:
Originally Posted by skipjack View Post
Grade Points
$\ \ \ $ A $\ \ $ 22-25
$\ \ \ $ B $\ \ $ 18-21
$\ \ \ $ C $\ \ $ 14-17
$\ \ \ $ D $\ \ $ 10-13
$\ \ \ $ E $\ \ \ \ $ 6-9

Ideally, D and E grades should be treated as unsatisfactory.
Here are my thoughts:

I can't really use the 'old-fashioned method' because the student having aced the quiz is a curve breaker. No curve would result.

I could say that I want the average score to be 85% and then use the following formula to change the maximum number of points from 25 to something else (denoted $x$):

$$\frac{\text{current class avg.}}{x} = \frac{\text{85}}{100}$$

The problem with the above is that my ace student would end up with 'extra credit' in contradiction to the terms of the syllabus, as would any other student with an actual score exceeding $x$.

Let's say I wanted a cutoff for those getting an A and I've decided that the top 8% of grades should earn an A. I believe then that I'm left with an integral I cannot solve (that of the probability density of the normal distribution), but could otherwise approximate:

$$\Pr( \,x \geq a) \, = \int_{a}^{\infty} \frac{1}{\sqrt{2\pi\sigma^2}} e^{-\frac{( \,x-\mu) \,^2}{2\sigma^2}} \, dx = 0.08$$

I'm not willing to go through some complex approximation process though. Further, after getting my approximation, I would have to convert the grades back to points because the overall grade is based on a point system.

That brings me back to your suggestion. How would I convert those grades you conjured above back into points as opposed to letter grades? I have no idea how you came up with that.

Ok, maybe I'm thinking about this too much, but also trying to nail down an approach I could possibly use going forward and technically even include in a syllabus (no, I won't be using Latex to create my syllabus ). I was curious if anyone here had a good method.
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