# Gas station without pumps

## 2011 July 27

### A is average

Filed under: Uncategorized — gasstationwithoutpumps @ 00:01
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Everyone has heard of schools and colleges that use the grading scale “A is average, B is bad, and C is catastrophic”.  But is that just a joke, or is there some truth to it?

A couple of weeks ago, Catherine Rampell published an article in the NY Times: A History of College Grade Inflation.  The article was based on “Where A Is Ordinary: The Evolution of American College and University Grading, 1940–2009” by Stuart Rojstaczer & Christopher Healy.  Unfortunately, the University library does not seem to have an electronic subscription to Teachers College Record (I don’t know how to parse that title), and I’m not willing to pay \$7 to read the original paper, so you’ll be getting a rehash of a rehash here.

Catherine Rampell included the following figure, which she credits to the original authors:

Figure by Stuart Rojstaczer and Christopher Healy, via the NY Times article. Presumably original caption: "Note: 1940 and 1950 (nonconnected data points in figure) represent averages from 1935 to 1944 and 1945 to 1954, respectively. Data from 1960 onward represent annual averages in their database, smoothed with a three-year centered moving average."

This is the guts of the article—grade inflation in college really ramped up in the late 60s, but has been getting steadily stronger from 1984 on. (Strange—I would have expected the doublespeak of grade inflation to have peaked in Orwell’s 1984.)

The increasing number of A’s is not due to an increase in the quality of college students.  If anything, the average intelligence and preparedness of college students has dropped somewhat as a greater fraction of high school students enter college.  What we’re seeing here is pure grade inflation.

I have no idea how the data were collected, but the abstract claims that data were gathered from over 200 colleges and universities.

There is a lot missing from this analysis (which may be in the original article).  For example, the abstract says that “science and engineering-focused schools grade more stringently than those emphasizing the liberal arts.”  How much of the grade inflation then, is due to shifts in what majors students are in (are there a greater fraction of students in the easy-A majors?) and how much due to grade inflation within majors?  It would be interesting to see historical curves like this that were not averages across all majors in all colleges, but broken up by major (or groups of majors, to avoid problems with small numbers). I think that there has been grade inflation even in engineering, with B- replacing C and C replacing D, but not nearly as bad as in the humanities, where A- has replaced B, and B+ has replaced C.

In one sense, grade inflation does not matter much, because no one really expects grades to be comparable between different generations any more. But there is a problem with loss of information in the grade.  The information content of a distribution with probabilities [0.35, 0.34, 0.14, 0.12, 0.05] is 2.04 bits (using $H= -\sum p_i \log_2 p_i$), but with probabilities [0.43, 0.34, 0.15, 0.04, 0.04] there are only 1.83 bits of information.  We get 10% less information from a grade than we used to, so we need 10% more courses to get the same amount of information.  Perhaps this explains the push for more and more education—as each grade gets less informative, we need more and more of them to distinguish the marginally competent from the truly incompetent.

A grading scale set up to inform us maximally about the students would have roughly equal numbers in each category, but we’ve never seen that in the US and are not likely to any time soon.

## 1 Comment »

1. It would also be interesting to see the grades by school year. I taught low level undergrad math at Univ of Montana for 10 years. Most of my students got A’s simply because the courses were way below their ability and knowledge level. The math placement test would place the kids in Precalc or Math 100 but after a couple of weeks the kids would remember what they had forgotten over the summer and breeze through the course. An extremely large percentage of our student population was placed in these lower courses so statically it would appear as grade inflation when in reality the course was just ridiculously easy for them. I imagine these low high school level courses could really skew the data.

Comment by Garth — 2011 July 27 @ 07:28

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