Item Response TheoryItem Response Theory (IRT) is the system used by Computer-Adaptive Testing such as the GMAT CAT to determine which question is the "best" next question based on the demonstrated ability level of the test taker. It is a statistical model that relates the probability of a test-taker correctly answering a problem to characteristics of the problem and the test-taker's true ability. It was first introduced in 1968.
There are three main parameters
- The ability of the item to discriminate between individual test-takers,
- The difficulty of the item, and
- The probability that the test-taker would get the question right solely by guessing.
Computer-Adaptive Testing Algorithm
Computer adaptive testing ("CAT") can begin when such an item bank exists. 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 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.
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.
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).
Tip #1: 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.
Unlike the old paper-and-pencil administered GMAT of the past, the GMAT CAT is better adapted to measure your ability with fewer questions. With the GMAT CAT, you answer only 41 questions for the Verbal section and 37 for the Quantitative section that are tailored to match your level of ability.
Tip #2: The first few questions you answer will either move you to a significantly more difficult or easy level; however, the last few questions you answer will only slightly increase or decrease in difficulty. You are given a question of moderate difficulty at the beginning of the test and first question in each question type. If you answer this question correctly, then the difficulty level increases. If you answer it incorrectly, the difficulty level decreases and this up-down system continues through the duration of the exam. The jump to a higher difficulty or the drop to a lower difficulty level decreases as you move through the test. Think of it as adjusting a lens. You first adjust the macro-focus to ensure you are in the right range of focus, and then you adjust the micro-focus to fine tune to reach the optimal focal point.
Tip #3: Please also bear in mind that there is a penalty for not finishing a section. The details have not been released by the GMAC or Pearson. But for each unfinished section, the penalty is about 4x the point for an incorrectly answered question.
Tip #4: Stay away from guessing in the beginning of the test. However, if you run out of time, then just randomly answer the last questions, at least you have 20% of the chance of getting it right for each question. If these questions are part of the trial un-scored questions, most likely the impact on your score is not that great. (Roughly 37 out of 41 verbal questions are scored, 33 out of 37 math questions are scored. So about 4 in each section are unscored.)
We need to caution you against guessing in the early stage of the test. Since your chances of guessing correctly are only 20% for each question, an incorrect choice moves you down to a less difficulty level very quickly in the beginning of the test. After a few randomly guessed wrong choices, the test assumes an appropriate level for you and it will be very hard for you to regain your momentum later as the CAT algorithm will not give you very difficult questions for you later to pile up some last minute points.
Tip #5: Please take particular care with the first few questions of each question type in both Verbal and Quantitative sections. Sometimes, it might be well into around the 10th question before you see a new verbal type question. Whenever you see that first question of a new type, slow down and do your best without unnecessarily spending too much time on it. Otherwise, you will have to rush through later questions.
Tip #6: Pace yourself! It is essentially a balancing act in which you need to slow down and give your best shot at the beginning and pick up the speed later till the end in order to maximize your score.
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