Test Score Metrics

Both of my kids recently took science tests and felt they didn't do well.  I asked them each, "Well, how did you do compared to the class average?"  Basically, neither was sure. Coincidentally, I am in the middle of grading a science test I just gave and thinking about where the class average is, what the distribution looks like and whether (and how) I should scale it.

In talking to my kids, I realize that my instincts on thinking about how well you did on a test being a relative thing comes from (1) being a physicist and (2) being a physics student.  Physicists know better than most that EVERYTHING is relative:  Velocity, Energy, Size, Temperature, Time, Length, etc.  But, more on point, test scores in physics tend to be low.  I don't know that I ever took a single physics test in 7 years of studying physics that wasn't scaled or manipulated in some way.  It's not uncommon in college but it is actually commonplace in physics.

Here's my favorite story about this (you'll see why shortly ;) ):

First year of grad school, CMU.  Dr. Russ's Quantum Mechanics course.  First test.  He folds the tests lengthwise after grading them for some reason and very soberly handed them back to us one by one.  As each of us saw our percentages we slunk down low in our desks and didn't make contact with each other.  I can still picture that big red 67% in a red circle beneath my name on that folded packet of work and feel it as defining me as a failure.  I'm going for a PhD in this stuff and I can barely eek out a "D"??  Russ doesn't say a work about the scores, just dives into talking through each of the problems and pointing out the niceties of solving them elegantly. Finally, my friend Dan Cormier from the back row tentatively asks "Dr. Russ - how did people do on this test?  What was the average?"  The professor looked a bit sheepish and says, "Well, I don't know the average, people did all right - it's tough material and there was a wide range of scores.... the high score was a ... a ... umm, Ken - what did you get  - was it a 67?  Yes, the high score was a 67."

Well, it isn't often you feel such a reversal of emotion.  I think I probably sat up straighter in my desk immediately after his answer.  My buddy Phil Koran called me "The Quantum Cowboy" for a few months after that.  Wonder why that nickname didn't stick??

So, kids - how did you do on your test, in a relative way?