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The Ins and Outs of Your GMAT Score II

Computer-Adaptive Testing Algorithm

As mentioned in our last week’s InFocus newsletter, there are three main types of statistics required of all items in an item bank –

1. a_i - the ability of the item to discriminate between individual test-takers
2. b_i - difficulty level, and
3. c_i - the probability that the test-taker would get the question right solely by guessing.

Computer adaptive testing (“CAT”) can begin when such an item bank exists. However, two more steps are required. First, the test-maker needs to select a procedure for determining test-takers’ ability estimates based upon their performance on the tested items. Second, the test-maker needs to choose an algorithm for sequencing the set of test items to be administered to test-takers.

An ideal item pool for a computer adaptive test would be one with a large number of highly discriminating items well distributed at each ability level. The information functions for these items would appear as a series of peaked distributions across all levels of ability estimate.

The CAT algorithm is usually an iterative process with the following steps:

1. Given the currently estimated ability level of a test-taker at a given point (usually the first question is started at mid ability level), the program evaluates all the items that have not yet been administered to determine which will be the best one to administer next.

   In this approach, the “best” next item would be the one that provides the most information about the test-taker. Typically difficulty level of an item is the most important parameter. However, in order to be able to clearly discriminate the ability among individual test-takers, the test-maker also incorporates other factors in the item selection process on a particular exam. They include different question types (data sufficiency vs. problem solving; critical reasoning vs. sentence correction), content (e.g., algebra, ratios, combinatorics, topic and inference questions for the same reading comprehension passage, etc.), and exposure (i.e., the number of times the question has been seen by other test takers already during a given period).

   Demonstrating to the CAT that you can handle a variety of substantive areas in all question formats will increase your GMAT score. The greater the variance among your ability in different tested topics, the lower your score. In other words, the GMAT rewards generalists—test takers who demonstrate a broad spectrum of competencies. This approach does make sense as in a business world, being well-rounded and knowledgeable can be positively correlated to a manager’s decision-making skills and managerial ability in general.

2. The "best" next item is administered and the test-taker answers

3. The program computes a new ability estimate based on the answers to all of the previous items

4. Steps 1 through 3 are repeated until a stopping criterion is satisfied.

We will continue with our analysis on the GMAT CAT scoring system next week.