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© Copyright 2000, Jim Loy
I was a bad student, but I was good at taking tests. Imagine this scenario:
I'm taking a tough Chemistry test. It is an hour long, multiple choice. I have to blacken in the answers on a computer "mark sense" form.
I do the test rapidly. I cannot figure out the answers to some questions. I make a guess, as a guess is better than no answer. And I mark these questions with an X in the test booklet. I am not sure of some answers. I mark these in the test booklet, too. I finish the last question. I look up, and people are leaving the room. They have finished the test. Only a half hour has gone by. I think to myself, "They are fools." They get B+; I am aiming for an A.
I go through the questions that I have marked. Ah, some of the answers were right. Some were wrong. Some, I'm still not sure of. But the number of wrong answers is surely dwindling. I look up again. Two-thirds of the students are gone. Fools. There's still ten minutes left.
I go back through the marked questions. I change one answer that I know was wrong; but I still don't know which is the right answer. And I correct another answer. I should have figured that one out earlier; it was easy. Still one minute left.
Let's work on one more question. Goll, I think I already got that one right. Time's up. I hand in my test, making sure (a second time) I put my name on it.
I got an A, by the way.
I have played tournament chess most of my life. I think chess trains you to take tests. It is not natural for a human to concentrate for a whole hour (or two). You have to train yourself. During a tournament, one player talked out loud. Several people went, "Sh!" They were distracted. I was distracted. But I went back to work on my move, and it was as if I had never been distracted. My analysis continued right where I had left off. I had trained myself to deal with distractions. Besides, it has been shown that chess increases a child's IQ. I recommend chess (and other thinking games and activities) as training for tests.
About guessing on multiple choice (or true/false) tests, here is an astronomy question that I didn't know the answer to (I do now, because I looked it up):
Which of these is the Stefan-Boltzmann Law?
a. F=GMm/R^2 (where R^2 means R squared)
b. L=4 pi R^2 s T^4 (where s is sigma)
c. E=hc/l (where l is lambda)
d. T=2GMm/3kR
Sorry about the notation; I am limited here by HTML and some people's browsers. Anyway, if I don't answer this question, my expected score for the question is zero. If I guess, without a clue, my expected score is 1/4. That is better. So I should guess on questions that I cannot figure out. But, I recognize answer "a" as Newton's Law of Gravity. So I can eliminate one answer. My expected score just went up to 1/3. Better yet.
What about tests where they penalize guessing. You get zero on the question if you don't answer it. And you get less than zero if you get a wrong answer. Normally, if you have four choices, the penalty for a wrong answer is 1/3. They take off 1/3 point for each wrong answer. That way, a guess is the same as not answering, in the long run. The expected score on each question is (1-1/3-1/3-1/3)/4=0. So your expected score is zero, either way. So they are not penalizing guessing; they are just neutralizing it. But if you have a clue (however shaky it is), then you should guess. In my astronomy question, I have eliminated one answer. So if I guess, my expected score is 1/9 ((1-1/3-1/3)/3), which is better than not guessing. I should guess, and risk the penalty.
Also, trust your judgment. Above I might eliminate answer "d" because I don't think it looks like a law. I might be wrong, but I must try. I'll choose "b" or "c." The correct answer is "b," by the way. I would probably have guessed "c" and got it wrong. Oh well. With many questions, I will guess some of them correctly. Also, I have done lots and lots of arithmetic (and algebra) by hand, or in my head. So, I sometimes can make educated guesses about how a correct answer should look.