Probably every couple years I have occasion to tell people “hey, did you know there’s some guy that tried to get the worst possible score on the SAT, on purpose?”

Well, there is. His name is Colin Fahey, and he writes about his experience on his web site. However, since last I looked at his web page he’s added some material on the mathematics of the SAT (multiple-choice guessing and the like, not the mathematics tested ON the SAT) and some, um, comedy.

Did you know:

1. the SAT has a “variable” section, which is not part of the student’s score but is used for research purposes. Section 5.6 of this document analyzes whether you can determine which section is the variable section during the exam; I’m reminded of what Wikipedia calls the unexpected hanging paradox (and what I call the “pop quiz paradox”, because I teach, although I’m not the sort of teacher who gives pop quizzes). I remember reading in SAT prep books that “you shouldn’t try to guess which section is the experimental section during the test”; I wonder if anybody actually goes to that trouble.

2. those “fill-in-the-blank” questions are really “12700-choice” (section 8)? What sort of person would work that out? (Okay, so I would have worked that out if someone else hadn’t already.) There are 22308 possible answers, but some of them (like `3..0`) don’t code for actual numbers, and others are equivalent (like `1/4_` and `0.25`, where `_` denotes a blank).

3. the distribution of the answers to said fill-in-the-blank questions (section 11.3) does not appear to be some nice, well-known distribution? This is true of exam questions in general, I think; answers tend to be close to unity. I gave an exam a few days ago where I asked students to compute the correlation coefficient of a small data set. The correlation was obviously negative, but the data did not fall on a straight line; the “simplest” guess, -1/2, would have been right.

4. Section 12.2 features a plot entitled “rough interpretation of the .52 correlation coefficient between the SAT combined scaled scores and college freshman GPA” (by the College Board); they seem to assume that SAT is a linear function of GPA plus a *uniformly distributed* error. Um, what? I’m not saying that the errors should be normal — I haven’t actually seen the data but I’m guessing there’s some compression at the high end of the GPA scale — but that’s at least a little more realistic.

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The idea of trying to get the lowest score on the SAT reminds me of one of my math courses, 18.25, Modern Algebra (groups, rings, and fields) at MIT my sophomore year. The grade for the course was based on three exams which were open book and open ended (they started at 7PM in Walker Memorial and the teaching assistants stayed until the last student left). They each consisted to 10 true / false questions. They were scored as +10 for a right answer, 0 for no answer, and -10 for a wrong answer, but with a score of +200 points for an exam that had 10 wrong answers. Needless to say, I knew more than a few bright and cocky students who scored -80.

By the time I was there that course was renumbered to 18.701, and the exams were a bit more conventional.