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Don't Worry About Grade InflationWhy it doesn't matter that professors give out so many A's.

By Jordan Ellenberg
Posted Wednesday, Oct. 2, 2002, at 10:38 AM ET

Last spring, George W. Bush reassured new Yale graduates, "And to you C students, you too can be president of the United States." He's out of touch. The gentleman's C, in Bush's day a respectably mediocre grade, is now a poor one. One study suggests that the average GPA in research universities and selective liberal arts colleges rose around half a point between the mid-'80s and mid-'90s. That grade inflation is taking place is hard to dispute. The question is: Should anyone care?

The arguments put forward against grade inflation span all genres: psychological (easier grading saps a student's will to achieve), moral (a weak performance is unworthy of the letter B), Marxist (grade inflation is a symptom of the consumerization of education), and even geopolitical (higher grades in the humanities draw American students away from the sciences, thereby compromising our ability to build better weapons and deflect other people's).

One of the most powerful and popular arguments against grade inflation is that it makes it difficult to tell one student from another. Harvey Mansfield, a professor of government at Harvard and a vocal grade-inflation foe, puts it this way: "Grade inflation compresses all grades at the top, making it difficult to discriminate the best from the very good, the very good from the good, the good from the mediocre."

That sounds reasonable. But it's wrong.

Start with a thought experiment. Suppose colleges offered only one grade, which we'll charitably call "A." Then all students would get straight A's. Indeed, the best and the very good, not to mention the so-so, are all in one box. Mansfield, so far, is vindicated.

Now suppose there are only two grades, which we'll call "A" and "A-," and suppose that, in each course, half the students get A's and half get A-s. Once again, the best, the very good, and the good, all look the same. The mediocre, perhaps, are weeded out. Mansfield is right, to a point; it's hard for him, in his class, with his grade, to distinguish one student to another. But college students take lots of classes. What happens on average over the four years of a college career?

Let's take a closer look at this two-grade experiment. Let Eva be a student who, on average, lands in the 70th percentile of her class. That is, 70 percent of students have weaker "natural ability" than Eva does. Of course, Eva will be better at some subjects and worse at others; there'll be some variation in her grades. We quantify this variability by supposing that the standard deviation of her percentile rank is 20. This means, extremely loosely, that the difference between Eva's actual percentile in any given class and 70, her "natural percentile," is "typically" about 20. For her to end up at the 30th percentile, two standard deviations below her average of 70, is an extremely unlikely event—according to the usual bell curve, Eva should score this low less than 3 percent of the time.

Now suppose Hans is in the 80th percentile of his class, also with a standard deviation of 20.

Both students are above average, and both will get mostly A's. But Hans, in order to dip below the 50th percentile and into the A- range, has to perform 1.5 standard deviations below his mean; this ought to happen about 8 percent of the time, or just two or three times in a standard, 32-class undergraduate career. Eva, on the other hand, gets an A- whenever she performs 1 standard deviation below average; this ought to happen about 17 percent of the time, which means Eva will rack up about 5 A-s. A seat-of-the-pants computation suggests that Eva has just an 18 percent chance of ending up with a higher GPA than Hans. Pretty good, for a system with only two grades!

Of course, this two-grade system is still helpless to distinguish between students Zoe and William at the 90th and 95th percentiles. Both have a solid chance of getting straight A's. But now suppose there are five grades, A through B- (A, A-, B+, B, B-), each attained by 20 percent of students. In this inflated regime, even gentlemen can coast to a B+ average! Let's say Zoe and William have average ranks of 90 and 95, again with a standard deviation of 20. Then one works out that Zoe should obtain, on average, 18 A's, 11 A-s, and three B+s, while William comes in with 20, 10, and two. Zoe gets a 3.83 GPA, and William a 3.86. Not much of a difference—but it's there—and admissions decisions have been made on much less. It's worth pointing out that, for our present purposes, it makes no difference whether the grades are labeled A, A-, B+, B, B- or A, B, C, D, F. Their discriminatory power is the same.

At this point, readers possessing technical proficiency and a mistrustful temperament will be piping up: Where do all these assumptions come from? How do you know what the standard deviations are? (I made them up.) Shouldn't the deviations be smaller at the top of the grade range? (I don't care.) And what probability distribution, exactly, are you using? (A truncated normal distribution, you fussy creature.)

Trust me: None of these questions matter. However you compute, the point stands. A grading scale much too coarse to separate students' performances in a single class (for instance, the system with just two grades) can—if it is not too coarse—be perfectly adequate when we have a whole transcript to look at.

How coarse is too coarse? It's actually easy to tell. In the example above, Zoe and William weren't separated on the two-grade scale, because both got straight A's. And, in general, a grading scale is too coarse if there are a lot of students who get the same grade in almost every class they take. In my experience, very few undergraduates make straight A's all through college, let alone straight B+s. That indicates that the present system, inflated as it is, is good enough to rank our students.

Indeed, a 2000 Department of Education study found that just 14.5 percent of undergraduates nationwide had a GPA above 3.75. And Henry Rosovsky and Matthew Hartley, in their well-reasoned monograph, found "no large body of writings in which, for example, employers or graduate schools complain about lack of information because of inflated grades." (Certain of their informants did complain to this effect in "informal conversations.") Anyone who's read fellowship applications, or graduate school admission folders, knows that the best undergraduates aren't hard to pick out—they're the ones who excel in nearly every course, the ones with a healthy sprinkling of A+s, the ones whose recommendation letters read like mash notes.

So, Mansfield is wrong—which doesn't mean grade inflation is all right. There are still those moral, psychological, Marxist, and geopolitical questions to think of.

And underlying all these questions is a deeper one: Why do we grade? Is the point to give students information? To reward, punish, or encourage them? Or just to hand them over to law-school admissions committees in accurate rank order? Until we answer this question, there's little hope of making sense of grade inflation. It's as if we were bankers trying to formulate a monetary policy, but we hadn't quite decided whether dollar bills were a means of economic transaction or a collection of ritual fetish objects.

"In a healthy university," Mansfield says, "it would not be necessary to say what is wrong with grade inflation." There, again, he's mistaken. In a healthy university, we would talk about every aspect of grading, down to the bottommost questions about why we grade at all. I suspect we'd all find it much less tempting, under those circumstances, to project onto our students' GPAs our anxieties about moral leadership, honesty, and the rewards to be expected from hard work. That would be an improvement. Grades are—should be—many things. But ritual fetish objects they are not.

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Jordan Ellenberg is an associate professor of mathematics at the University of Wisconsin. His first novel is The Grasshopper King.
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Notes From The Fray Editor:

Fray grade inflation? No, the proliferation of check marks here only indicates what the posters already know: this is a terrific discussion. I have appended accounts of missing assumptions, real-world after effects, Meph's argument against grades altogether (the whole thread is very good) and Michael's well-wrought thought experiment. Update: Author Jordan Ellenberg has responded to Michael's experiment below.

Remarks From The Fray:

As one who teaches college juniors and seniors and must deal daily with their grade anxieties, I only hope I live long enough to see the grading system wind up on history's trash heap where it belongs. Ellenberg's analysis, which some might take as vindicating the system despite inflation, is fallacious in this respect: It "snapshots" grade inflation at a given moment, instead of treating it as a dynamic phenomenon -- one which, like monetary inflation, feeds on itself and therefore becomes "runaway." Nowadays students argue (vehemently; I just had two of them doing this yesterday) if they get a B+. To instructors like myself who don't have tenure and are hostage to students' good opinions, this creates pressure to inflate FURTHER; I've already inflated grades as if they were the tires on an 18-wheeler, but it's never enough. Eventually A- will becomes the grade that students find unacceptable, then A, and at that point (Lord, I hope) the system's absurdity will become so obvious that even a college dean can grasp it. So even if Ellenberg is right and the system can still distinguish among students in its current state, the point is that its current state is inherently unstable and self-destroying.

-- Professor Moriarty

(To reply, click here.)

I hire computer science graduates to work in my department. I wouldn't want to hire any that didn't excel in their intro to computer science courses and who didn't excel in some of their senior year courses. But is a B+ a good grade? How about an A-? Is A average and should I be looking for A+'s?

-- rob

(To reply, click here.)

Finally, there's the general problem of being honest to the rest of the world. Most people don't know that the vast majority of Harvard students graduate with honors, or that a high -by traditional standards - GPA doesn't really mean much. So by handing these things out freely universities are perpetrating a small-scale fraud on the rest of the world. It's a common enough offense, like the bank labelling the clerk who fills out a form to decide if you get a car loan a "vice-president," but that doesn't make it OK.

-- Bernard Yomtov

(To reply, click here.)

What happens to students who attend schools where grade inflation does not occur when they are forced to compete with students where grade inflation is rampant?

-- Alan

(To reply, click here.)

He assumes that all classes at the college have pretty much the same grade distribution; under this assumption, grade inflation just results in a compression in overall GPA at the top of the scale, but doesn't eliminate all GPA differences between top students.

But suppose there are a few classes which have tough professors, determined to resist grade inflation. To dramatize the point, suppose that most reasonably good students (say, 80th percentile) will get a "C" in these courses, as opposed to the "A-" they would be getting in their other courses. A reasonably good student might expect to lose a tenth of a point or two in overall GPA by taking a few such courses.

With an uninflated, uncompressed grade scale, a tenth of a point might not mean that much, and the student might decide the course was worth it. But the more the grade point scale is compressed, the *bigger* the relative effect of the outlying courses will be.

-- Alex R

(To reply, click here.)

The author misses the point. Numbers like 3.86 and 3.83 and 3.1415692 don't tell you anything about the student. What classes were they strong in? What areas of what classes did they do well in? Grades, whether inflated or not, communicate next-to-nothing about the student.

The solution, the obvious solution, is narrative evaluations. I had them in college (UC Santa Cruz) and a narrative evaluation -- a paragraph or two describing the student's performance -- is far more helpful to a prospective employer or graduate school since a stack of evaluations will reveal whether the student's strength is test-taking or writing papers, whether the student participates in class, and so on.

-- Meph

(To reply, click here.)

Numb-nut's argument doesn't hold water. By narrowing the range of grades actually given, grade inflation does hurt the ability to evaluate a student based on grades.

Thought experiment:

Imagine two students whose performance in various classes are reflected by the following percentiles (compared to other students):

Student A
100, 95, 98, 67, 90, 98, 86
Student B
70, 75, 80, 71, 77, 82, 90

Which is the better student? I think it's pretty obvious it's student A. In a grading system that makes full use of grades all the way from A down to F-, in roughly equal proportions, this will be very clear:

Student A
A, A, A, B-, A-, A, A-
Student B
B-, B, B+, B, B, B+, A-

However, now think of a grade-inflated system, where 90% of all students get A, A-, or B+ (in roughly equal numbers):

Student A
A, A, A, A-, A, A, A
Student B
A, A, A, A, A, A, A

Not only does the grade-inflated system deprive Student A a chance to benefit from his relative excellence compared to student B in five out of seven classes, it actually makes student B look superior, based only on him having never performed under the 70th percentile. Rather than rewarding excellence, it rewards mere consistency. If you were to consider one of these two students as an employee, it's awfully clear that, other things being equal, Student A would be much prefered if you had access to the raw data, whereas Student B will look better when the precision of that data is destroyed through grade inflation.

Surely the columnist realizes this, which makes me wonder why he's intent on playing mathematical games here.

I'll bet that if we could put money on this, he'd admit his error. For example, let's say we put together a diverse battery of 30 intelligence tests, each covering a different field of knowledge. 100 people would take each of the tests, and the columnist and I would have access to the scores, and then would pick an "academic decathlon" team of 25 each, with the teams competing and each of us wagering $10,000 of his own money. Let's say we have a choice, we can get the test results for each student down to a precision of 1 percentile, or we can get the results generalized to "above average", "average" and "below average". Having to put his money where his mouth is, does the columnist really contend that it doesn't matter? He'll just pick the people who got the most consistent "above average" scores? For my own part, I'd want to know down to the nearest percentile, in selecting my team. I'd want to be able to tell the difference between the 99th percentile scorers and the 67th percentile scorers.

I can't imagine that any scientist worth his salt would feign indifference as to the precision of his instrument, and the same should be true in the science of measuring academic performance.

-- Michael

(To reply, click here.)

Michael and his sensitive testicles are correct: the grading scale he describes, which gives the top possible grade to a third of students, would be too coarse to separate students A and B.

If students A and B were typical of the current grading regime, then large numbers of students would have transcripts consisting almost wholly of A's. In my experience, this isn't the case, and I don't know of data that shows it to be the case.

What's atypical about the students Michael imagines is their "mere consistency," which is actually rather extraordinary. Student B finishes between the 70th and 82nd percentile in 7/8 of his classes. This, again, runs counter to my experience in teaching. I don't feel confident predicting that a student in the 75th percentile in my calculus course is particularly likely to land between the 70th and 80th percentile in her writing seminar.

I actually think Michael's proposed wager makes his point, and mine, more clearly than his thought experiment does, so let's move on to that.

He may well be right that a system with only three grades is too coarse for the project he describes. However, that doesn't mean that more grades are always better. There comes a point of diminishing returns; where that point is is not determinable by pure thought, but depends on empirical facts about the particular system one is trying to measure.

Let me put it this way: would Michael put up $20,000 against my $10,000 if I agreed to learn my candidate's scores only within 2 percentiles, while he still knew his within 1?

General note: I agree with J.D.: this was a particularly fine Fray.

-- Jordan Ellenberg

(To reply, click here.)

(10/4)

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