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The Fallacy of Hard Tests

kudos200 Is the math entirely wrong? (404 comments)

Is the math in this article entirely wrong, or am I just crazy??

For True-False exams for example, the number subtracted would most likely be (Number Wrong ÷ 2). Let's see how that would work out, for the sample case above. You, answering two questions correctly and guessing at 98 would be likely, on the average, to get 49 wrong, and so have a final score of 2 + 49 - (49 ÷ 2), or 75.5, while I, again on the average. answering only 1 correctly and guessing at 97, would get a final score of 1 + (97 ÷ 2) - ((97 ÷ 2) ÷ 2)), which comes out to be 25.25. Here there is a substantial difference between our scores, closer to the two-fold difference in our actual knowledge.
2 + 49 - (49 / 2) is equal to 26.5, NOT 75.5 . . . he added it in one case and not in the other. So the actual scores that should be compared are 26.5 to 25.25. The disparity he saw was entirely from a lack of capability at arithmetic. And in all his examples, the numbers are so close not because of a lack of quality in the testing methods, but because his hypotheticals are so extreme (someone who only knows the answer to 2 questions out of 100 is ridiculous). That said, subtracting for wrong answers is still the most accurate way to grade, but not based on the crap that this guy was talking about.

more than 7 years ago

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