When I took my high school’s AP Calculus classes these last two years, the teacher pointed out that since, on average, guessing would give the same result as leaving questions blank, you might as well guess. As far as I know, nobody disagreed with him.
(Actually, he said it’s better to guess, because leaving a question blank means running the risk of accidentally putting the next question’s answer in the wrong place—which, in one case, led to a student answering practically every question in one section wrongly. But that’s relatively impertinent.)
Hmm. And why is the parent comment downvoted? It’s incorrect to obviously agree with a sweeping assertion that the “result” is the same if expected score is the same. The expected utility of the outcome is going to be strictly higher or lower from following one of these strategies, it’s not going to be the same.
For an exam where what matters is your grade relative to other test-takers, like the SAT, probably yes, but on an exam with a hard pass/fail threshold, the utility function is discontinuous (and therefore non-linear) around the threshold, so guessing might make a difference.
Ah, good point. I always forget ‘get the highest score possible’ isn’t everyone’s goal; presumably, some people would prefer 70% and 100% about equally in this case.
It is about the ‘expected’ part. The average of utilities for each score does not have to equal the utility of the average score. It is only equal when utility scales linearly with score.
Guessing, if you have no idea which way to guess is more likely, will not have quite the same result as leaving questions blank. Leaving questions blank will add 0 to your score, while guessing will add a mostly-Gaussian random variable with a mean of 0. The math of this is kind of fun:
When I took my high school’s AP Calculus classes these last two years, the teacher pointed out that since, on average, guessing would give the same result as leaving questions blank, you might as well guess. As far as I know, nobody disagreed with him.
(Actually, he said it’s better to guess, because leaving a question blank means running the risk of accidentally putting the next question’s answer in the wrong place—which, in one case, led to a student answering practically every question in one section wrongly. But that’s relatively impertinent.)
The same expected test score doesn’t imply the same expected utility.
Hmm. And why is the parent comment downvoted? It’s incorrect to obviously agree with a sweeping assertion that the “result” is the same if expected score is the same. The expected utility of the outcome is going to be strictly higher or lower from following one of these strategies, it’s not going to be the same.
Presumably, as long as you’re not equivocating on ‘expected’, that isn’t true. For tests, ‘test score’==‘utility’, no?
For an exam where what matters is your grade relative to other test-takers, like the SAT, probably yes, but on an exam with a hard pass/fail threshold, the utility function is discontinuous (and therefore non-linear) around the threshold, so guessing might make a difference.
Ah, good point. I always forget ‘get the highest score possible’ isn’t everyone’s goal; presumably, some people would prefer 70% and 100% about equally in this case.
It is about the ‘expected’ part. The average of utilities for each score does not have to equal the utility of the average score. It is only equal when utility scales linearly with score.
Guessing, if you have no idea which way to guess is more likely, will not have quite the same result as leaving questions blank. Leaving questions blank will add 0 to your score, while guessing will add a mostly-Gaussian random variable with a mean of 0. The math of this is kind of fun:
http://en.wikipedia.org/wiki/Random_walk
And of course, the central limit theorem is colossally important:
http://en.wikipedia.org/wiki/Central_limit_theorem
No need to invoke that here—directly calculating the probabilities using the binomial distribution is perfectly practical in this instance.
Practically every question, or about half?