Last week, we continued our discussion of the "item characteristic curve," which ETS uses to determine whether a particular question is appropriate for you at a given point during your exam. This week, we will discuss the "inverse item characteristic curve" as well as the "estimator curve," both of which serve to help the CAT find your score.

If you recall, the item characteristic curve displays the probabilities of answering a particular item correctly for different ability levels.

The "inverse item characteristic curve", on the other hand, displays the probabilities of answering a particular item incorrectly for different ability levels. If, for example, the curve for an item indicates that someone performing at the 600-level has a 45% chance of answering the item correctly, the inverse curve for that item would indicate a 55% chance of answering the item incorrectly. This is because the probability of answering correctly and the probability of answering incorrectly must sum to 100%, since those are the only possibilities. In essence, then, each point on the inverse curve is simply 100 minus the probability of answering the item correctly for that ability level.

What is the purpose of the inverse curve? After every question, the CAT takes all the regular curves for the items you answered correctly and all the inverse curves for the items you answered incorrectly and multiplies all the curves to arrive at the "estimator curve" of your ability. Basically, the CAT determines the probability of your answer pattern by multiplying the regular and inverse curves.