User: ThematicDevice

Error in the Math

On: The Fallacy of Hard Tests

[i]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.[/i] Lets think about this, 51-24.5=26.5 not 75.5, further, knowing one would mean guessing at 99, not 97. 1+(99/2)-(97/4)=25.75 This means the avg. difference if adjusting for guessing moves from .5 (average score of 50.5 vs 51) to .75, hardly a substantial difference. Of course the numbers will separate out at greater levels of knowledge as he showed earlier, if one person can answer 50 and the other 25, the average scoes will be 62.5 and 43.75 Now he probably simply didn't check his math, but twice in the same paragraph?