The College Board is changing its scoring method for 5-way multiple-choice questions on the AP exams from to . The new system is easier to explain to people, but introduces a bias in the scoring.

Previously a student who knew nothing could either leave the question blank (score 0) or guess (0.2 change of getting a 1, 0.8 chance of getting -0.25, for an expected value of 0 and standard deviation of 0.5). Students who knew anything at all were better off guessing. Now all students are much better off guessing, even if they know less than nothing (that is, even if their chance of guessing the right answer is less than the uniform 0.2, they are still better off guessing).

Essentially, all students are now forced to guess, as the system has switched from one in which guessing was neutral to one in which guessing gets a bonus. Put another way, AP has introduced a penalty for leaving questions blank. This change is likely to have a gender-biased effect, as girls were more likely to leave questions blank when they didn’t know the answer, and boys more likely to guess wildly.

Since no one uses the raw scores, the shift in raw scores is completely irrelevant. Forced guessing will increase the variance on the exam scores slightly, and cautious students will be penalized substantially until they learn to guess even when they know that they have no idea. I can’t see any advantage to this change.

I think that the problem that the College Board is trying to address is one of terminology. For years, people have incorrectly called the neutralization of guessing a “guessing penalty”, when there was no penalty for guessing (expected value same as leaving question blank). So now we’ll have a guessing bonus instead.

Note: I’ve also heard that the AP test is going from 5-answer multiple choice to 4-answer multiple choice, supposedly to make the test easier. Why is that a desirable result?

I’m only aware of 2 tests that have a real guessing penalty, the AMC-10 and AMC-12. On those tests, the scoring is for an expected value of 1.2 if guessing randomly, and 1.5 if left blank. Reducing the choices from 5 to 4 would give a neutral value to guessing (that is, if they can increase the probability of getting the right answer from 0.2 to 0.25, it is worthwhile to guess). On the AMC-10 and AMC-12, test takers do have to think about whether they really know anything about the answer before guessing. Personally, I would have preferred to see which would have an expected value for guessing of and 0 for leaving questions blank, but I guess that the test designers wanted to have only non-negative scores.

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