Best Guess

Something of a historical nature today.

When I was a kid in school, multiple choice tests were popular. I presume they still are just because they are so easy to grade – either you selected the right answer or you didn’t. They even had electronic “scantron” systems that could grade it for you. Yet when I was teaching later I never used them…

It was common for kids to refer to them as “multiple guess tests”. Me, I generally didn’t guess. I had the highest IQ my small local school had ever seen and at one point I’d read the entire Encyclopedia Britannica; if I had to guess no one there knew the answer.

But I did say “generally”. With my IQ, the school wanted me to participate in every contest they could find, even as a sophomore (grade 10 if you don’t use that term for high school). Of course the ACT, SAT and PSAT, but even ASVAB (armed services vocational aptitude battery), National High School Math Exam (twice, as a sophomore and a junior) and anything else they could.

One of those contests was called the Junior Engineering Technical Society test. You could actually take two subjects – of course I was taking Math as one. The other … for reasons of not having anyone else who wanted to take it in that subject they suggested I take it in Physics, though actually Physics was a senior level class at that school and I was a junior. I had been exceptional in General Science 2 years earlier and I liked books about physics, so I figured it couldn’t be too bad, right?

Well, the contest in this region was held at BGSU on a Saturday, and the Math test was first. I felt pretty good about that one, though my school didn’t have any Advanced Placement courses so I wasn’t really spectacular. I got done in time and did good, that’s about it.

Physics … turns out I had no idea how to do most of the questions. While I understood the concepts, I didn’t have the formulas to compute the answers they wanted. Well, I wasn’t going to sit there for 2 hours just to leave the test blank, so I started looking for patterns in the answers.

Years later I actually had classes in designing multiple choice tests. The idea is to have 3 or 4 reasonable answers (answers you might get if you made some small error in the computations) and then one or two “distractors”. I didn’t actually know it at the time of this test, though it was pretty easy to spot. They’d have answers that were multiples of each other – one twice the other, one with a different exponent (of course they were in scientific notation) … so it made sense to pick the one that had the most common exponent with the most common decimal part. Of course they weren’t all like that – there was one where they were trying to see if you could figure out what units the answer should be in, for example. I did know that – I could tell the question required an answer that was a volume and only one answer had the right units.

Needless to say, since I wasn’t doing any of the calculations I actually got done first. Anything that I didn’t have a clue on I guessed, so nothing was blank, but I couldn’t say at the time how I did.

There was a break for lunch then they announced the winners. I wasn’t mentioned in the Math results – I wasn’t in the top 3; that’s all I know there. Physics … turns out I was second. I knew nothing at all about the subject, and only one person did better.

There are books and even short classes in “test taking”, obviously I’d figured it out on my own from all the other tests I’d taken before that. Though also obviously after that I had no respect for multiple choice tests at all.

5 Replies to “Best Guess”

  1. At my university, we were required to take some complimentary subjects in addition to the main ones we were taking for our degrees. I always remember that one particular complimentary subject was assessed by a single multiple-choice test. Every question had 4 possible answers. The test must have been either very cleverly designed, or extremely poor, because some people always got less than 25% in it, which I’m sure you’ll have already noticed is the grade one would typically expect from random-guessing!

    The last time I did a test with a multiple-choice component, it was to obtain a formal certificate in a field I already have “hands-on” experience in. It was rather frustrating because some of the questions were a little unfair. It was on a particular piece of legislation that I know inside-out because I work with it every day. Due to flawed and occasionally-ambiguous wording of the potential answers, it meant that not a single one of the options was actually correct, because they all contradicted the actual text of the legislation! I had to guess the most likely response based on how well I believe the examiners knew the legislation, and the differences between their native language and English (the language of the test). I later found out I got the answer “wrong” for some of those questions! Fortunately I passed based on the merit of the prose and calculation sections of the exam…

    When I was a teacher i almost never offered multiple-choice tests to the class. I far preferred simple calculations or explanations. For less-able students, I favoured questions of the format, “John thinks that……….. but Jane says ……………. . Who do you agree with? Explain why”. As a teacher, I always felt it was more important to work out what’s going on in your student’s head to arrive at an answer, than the correctness of the answer itself.

    1. Never done that kind of stats? Just because the average by guessing is 1 in 4 does not mean that’s what any one person will get. My old handbook says the standard deviation on a binomial distribution is SQRT(npq). So say your test has n = 100 questions with p = 1/4 and q = 3/4, then sigma = SQRT(75/4) = 4.33

      That means some 68% of the tests will have a score of between 20.67 and 29.33, while 16% will have gotten 20 or below (and another 16% 30 or above) – just by guessing.

      If you see someone actually got 15 or less you might wonder if it was intentional, but a score of 20 is just bad luck.

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