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How the GMAT finds your score, part III

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How the GMAT finds your score, part III

Post Mon Jul 17, 2006 8:59 am
This week we will continue our discussion of the "item characteristic curve", focusing on the significance of its steepness. Specifically, how does the steepness of the curve change when you answer an item correctly? Here is the curve again:



Notice that the curve suddenly becomes steep between 600 and 700 along the ability axis. The sudden pitch at this point indicates that ETS considers the difficulty of this item (remember that ETS refers to questions as "items") to correlate with an overall ability level between 600 and 700. In other words, ETS believes that this item represents the greatest level of difficulty that someone scoring in the 600 to 700 range could handle with a greater than 50% chance of success.

As items increase in difficulty, the steep part of the curve moves farther to the right. So when you answer an item correctly, the next item you see will have the steep part of its curve farther to the right. By the same token, when you answer an item incorrectly, the next item you see will have the steep part of its curve farther to the left.

So let's assume a certain test-taker has been performing at a relatively high level, corresponding roughly to an overall score of 640. The next item she sees could very well have the curve shown above. Now let's assume that she answers this item correctly. The CAT will then select an item whose curve will have its steep part slightly farther to the right, indicating that a correct answer for that item demonstrates an ability consistent with a slightly higher overall score. However, keep in mind that items appearing earlier in the exam contribute more assessment information than do later items. This means that correct answers early in the exam move the steep part of the curve farther to the right than do later items. For example, if the item shown above were, say, the fourth item on an exam, a correct answer would probably move the steep part to a range corresponding to an overall score of 680 or 690. If this item appeared as the twenty-fifth question, a correct answer might move the steep part to a range corresponding to an overall score of "only" 660.

Why is this? Because by the time you have answered twenty-five questions, the CAT has gained significantly more information about your ability than after only four questions. Correct answers later in the exam will not cause the steep part of the curve to move as far to the right because the CAT is already zeroing in on your precise level. Earlier in the exam, the steep part moves farther because the exam is giving you the "benefit of the doubt." That is, the CAT "thinks" to itself, "Because I do not know you, I was not expecting you to answer this item correctly, so perhaps your ability level is 70 points higher than I thought." After twenty-five items (a somewhat arbitrary number), the CAT "thinks" to itself, "I have seen you answer twenty-five items, so the fact that you answered this item correctly makes a small difference in my assessment of your ability."

Imagine the exam as a baseball game. If a player hits a homerun the first time at bat, your initial impression of his ability will be pretty high, though it is certainly possible that he will lose your goodwill by fumbling easy plays later on. If, however, that player is mediocre for eight innings, a homerun in the ninth (let's assume it is not a winning run) will certainly improve your assessment of his ability, but you are already predisposed to think of him as a player of a lower caliber and the homer will seem like a fluke.

What happens, though, when you answer an item incorrectly?

Next week, we will discuss the flip side: the "inverse item characteristic curve."

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