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Thursday, May 31, 2012

A is for Average


Don't take this entirely too seriously.  I saw the chart at Wm. Briggs, Statistician to the Stars! and followed it back to Gradeinflation.com but I did not dig into the data.

The average grades given for each year by a sample of 79 colleges over the past near-century. Data for the 1930s is sparse, being only about 8 colleges.  So it may also be that not all schools are present in all years, esp. in the early part of the graph.

Now here is a remarkable thing regarding infantile regression.  Take a ruler -- not a king, but a straight-edge -- and place it over the period of the 1940s.  You will notice two things:
  1. There is not a linear trend.  The 1950s bent down; there was a sudden shift starting in the mid-1960s, flattening out after the mid-1970s, and then climbing steadily since about the mid-1980s.  
  2. If you extrapolate from the 1940s, the red overall averages after 1985 falls exactly where your straight edge would have put it had the 50s-60s-70s roller coaster never happened!  'Sup that?
  3. A third thing is that a grade level gap opened up between private colleges and public colleges in the 1960s.  Either private schools like Harvard are easier graders than public schools like Ohio State or else the private schools began getting a smarter student body
That might be.  Prior to the 1960s there was no expectation that everyone should go to college so public and private were probably harvesting a similar crop of applicants.  As the great mass of average students sought college -- and a 2S Draft Status! -- they may have entered the public schools in greater numbers. 

If pushed, or nudged with a sharp elbow, TOF might be inclined to say that, in addition to random variation and school-to-school variation (the gray dots!) there are two things happening. 
  1. Grade inflation, as marked by the trend in the 1940s and emerging again after the 1980s.
  2. A perturbation to the process that caused the system to "bounce around" before settling back on the underlying trend. 
Caution: The grade data will be serially correlated.  Two successive points are NOT independent and identically distributed variables (iidv).  In any two successive years, most of the professors giving the grades, as well as about 75% of the students earning them, will be the same.  Because two major factors in grade assignment (the profs and the students) are at least mostly the same from one year to the next, the outcome (average grades) are also mostly the same.  Faux-trends and -runs appear more often in serially correlated data than in iidv data. 
You can see the same sort of perturbation behavior in other data. 

US Birth Rates. The trendline is a sine wave coasting down an decaying exponential curve.  But in 1919 there is an icicle, because in 1918 the guys were off in France doing guy things.  Then in 1920-21, the rates spiked above the trendline as all the horny soldiers came home before in 1922 returning to just where the sine wave would have taken the rates had there been no perturbation in the first place.  A similar, though bigger dip-spike-normal patters holds in the years after Pearl Harbor.

% Women in the labor force.  The trendline is an exponential growth curve.  The spike representing Rosie the Riveter drops right back to where the curve would have wound up without the spike. 


6 comments:

  1. I confess I find myself highly skeptical of the notion of 'grade inflation'; there certainly have been shifts, but I think thinking of it as an inflation usually involves assuming that there's a unified thing to be inflated, when in fact there never was, and this is even less true today. Grading policies vary from school to school, and often school grading policies are loose enough that they can vary considerably from professor to professor in the same school. And even where the policies are very strict, it doesn't make much sense to treat an A in electrical engineering as if it meant the same thing as an A in creative writing, if it were even possible to figure out a way to give such courses a common measurement.

    My own suspicion -- it is only such, of course -- is that what we're really seeing is shifts in agreements over assessment methods and grading philosophies; e.g., as professors have been encouraged to be more creative with their classes and allowed to be more creative with their assessments, everyone has gone their own way (the gray dots, as you note). And it's possibly notable that the pattern of difference among private, public, and community colleges is pretty much the pattern you'd expect in terms of how much freedom professors are allowed for deciding their own policies.

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    1. Maybe this is my ignorance speaking, but Brandon's strikes me as a sound analysis.

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  2. Are we missing a third chart?

    Also, picked up In the Lion's Mouth from Larry Smith at Balticon but haven't started it yet, though it's in the queue.


    JJB

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  3. IMHO, the Vietnam war accounts for the rapid increase in average GPA seen during that same period. Attending college meant not being subject to the draft. College professors, who were by and large anti-war, awarded grades so as to avoid flunking students out and thereby eliminating their deferment. The consequence was to significantly raise grades on the low end, thereby raising the average.

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  4. The graph and analysis are interesting. But the problem is that (like Lisa Simpson) we've gotten to the point where we need to add multiple plus-signs to the grade of A in order to distinguish the exceptional from the merely pretty good.

    A survey published in the Teachers College Record and discussed in Inside Higher Education doesn't look at GPA but at how often the grade of "A" is assigned. The frequency ranges from 39% at public, commuter schools to 48% at private, non-profit colleges and universities.

    Yes, you read that right. 40% plus of all undergraduates are being awarded the grade of A. A substantial majority of the remaining grades are B's, with C/D/F grades making up 15-25% of the total.

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    1. Sorry, that was sloppy. 40% plus of all course grades assigned to undergraduates, not 40% of all undergraduates.

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