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How the GMAT finds your score, part II

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Kevin Community Manager Default Avatar
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How the GMAT finds your score, part II

Post Mon Jul 10, 2006 8:18 am
Last week we discussed the "item characteristic curve" in very broad terms. This curve is the driving force behind the CAT's assessment of your ability. What does the shape of an item's curve indicate about one's performance at that point in the exam?

Here is the curve again:


Each question that you see on your GMAT has a curve like this. The curve contains information about the likelihood of getting the question right based on data collected during that question's experimental phase. For this particular item, for example, someone with a 500-level ability (meaning that he or she performs at a level consistent with an overall score of 500) has a 30% chance of answering correctly. Someone with a 600-level ability has a 45% chance, someone with a 700-level ability has a 90% chance, and someone with an 800-level ability has a 95% chance. Since the CAT seeks always to present items for which you have a 50% chance of success, this item would be presented to someone who is performing at a level that the CAT is estimating to be somewhere between 600 and 700, since the 50% mark falls between those levels for this item.

The curve does not begin at 0% probability because of what is known as the "guessing parameter", which is just a fancy way of describing the minimum probability of answering correctly with a random guess. Since there are five answer choices, a random guesser has a 1/5 chance of answering correctly. So the baseline probability for answering an item correctly is 20%.

Notice that the probability of answering correctly jumps significantly in the curve above as ability level increases from 600 to 700 (45% to 90%). The steepness of the curve between these ability levels indicates that this particular item can be used most effectively to zero in on a precise level between those points. During the item's experimental phase, performance on this item changed dramatically as ability level increased from 600 to 700. At the extreme ends of the score range, however, the probabilities do not change that much. Therefore, this item is not as useful to distinguish a 700-level test taker from an 800-level one, since both are quite likely to answer this item correctly. However, someone with a 600-level ability is much less likely to answer correctly than is someone at the 700 level.

An item, such as this one, whose curve has its steepest part between 600 and 700 can be considered a "threshold" item (this is not ETS terminology) for the 600-700 range, for example. This means that when the CAT needs to determine whether its estimate of your ability should be closer to 600 or to 700, it may very well select this item to refine its image of your capabilities. If you get it right, the CAT will move its estimate of your ability towards 700. If you get it wrong, your estimate will move towards 600. In essence, your estimated ability is a fluid concept to the CAT: it is always changing, based on your performance on the "threshold" items for various ability levels.

The curve retains its basic shape from item to item as the exam progresses, though the location of the steep part changes. Next week, we will discuss in detail how the steep part changes when you answer an item correctly and what the change indicates about the CAT's assessment of your ability.

_________________
Kevin Fitzgerald
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Manhattan GMAT
800-576-4626

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