Computerized Adaptive Testing and Calculating Your GMAT Score

By - Feb 24, 13:28 PM Comments [0]

It is important to understand how the GMAT calculates your score, and what this means for you as a test-taker.


Fact: The GMAT uses Computerized Adaptive Testing (CAT)

This means, first of all, that each question you answer right or wrong determines what questions you will see later in the GMAT.  It also means that any two people, even two people of nearly identical abilities and preparedness, will not see identical questions when they take their respective GMATs.  BUT, because of the magic of psychometrics, two people who perform with comparable skill & strategy & focus will have comparable GMAT scores.  The magic of how the test is different for everyone but the score is fair for everyone --- if you don't have a Ph.D in Psychometrics or Statistics or something like that, then just take that magic as an article of faith.


How does CAT work?

The GMAT is trying to figure out objectively your Quantitative Ability and your Verbal Abilities in a relatively short time.  Think of it as a big "twenty questions" game.  Suppose your "opponent" picks a US city, and you are allowed to ask "horizontal yes/no questions" (e.g. "Is your city east/west of X?") and "vertical yes/no questions" (e.g. "Is your city north/south of X?).

You might ask a bunch of horizontal questions.  It is west of Albuquerque? No.  Is it east of Atlanta? No.  Is it east of Denver? No.  Is it east of Santa Fe? No. OK, that narrows things down to a relatively thin band.

Then a bunch of vertical questions.  It is North of Wichita? No.  Is it north of Birmingham, AL? No.  It is north of New Orleans? Yes.  Is it north of Tucson? No.

Among major cities, those answers are enough to hone in on El Paso, TX.  Much in the same way, the GMAT asks you two question types, Math and Verbal.  By giving you easy & hard questions of each kind, it hones in on what is most appropriately your level.


Not so exact

That analogy is helpful for understanding CAT, but the problem is: things are not that exact.  If we want to know where a city like El Paso is, that's totally objective, and the questions about whether such-and-such city is N/S or E/W of El Paso are also totally objective.  That means, with very few questions, one could hone in on an exact location.

A person's math & verbal ability is not so precise a thing.  First of all, there are easy questions you definitely can answer, there are super-hard questions you definitely can't answer, but for the questions in-between, it's gray: there's a difficulty level at which you usually get questions right, another slightly higher at which you usually get the questions wrong.  For the sake of argument, let's say that we have figured out questions that are exactly at your ability level if, on average, you get questions at that level right 50% of the time.  Clearly, whether you answer any one question correctly or not is not enough information to tell whether it's at your ability level or no; determining your level is going to be about an average over several questions, not simply the answer to one.  Furthermore, there are frequent aberrations.

Super-brilliant people sometimes get an easy question wrong, and folks who are minimally prepared can still guess correctly on one of the toughest questions.  With statistics, the computer can absorb such aberrations.  What the computer is doing throughout your test is averaging over the difficulty ratings of all the previous questions, using the data about which you got right and which you got wrong to create a complex average that is the best estimate of your ability, and each new question it feeds you is the computer's attempt to refine that best estimate.

Your score is a composite result that takes into account the difficulty of each question you got right and the difficulty of each question you got wrong.The exact details of the algorithm that the computer uses to do this are (a) probably incomprehensible if you don't have a Ph.D. in Statistics, and (b) the secret proprietary information of GMAC.  Legally, we don't have access to thatalgorithm, and in likelihood, even if we knew, we probably wouldn't understand it anyway.


Facts vs. Myths about CAT

Fact: If you get medium questions mostly right, the computer will start to feed you harder questions; if you get medium questions mostly wrong, the computer will start to feed you easier questions.

This is true.  The CAT adjusts to your level throughout – much like the E/W and N/S question in the geography game above, it is constantly refining its picture of your ability, question by question.


Myth: If I suddenly get a ridiculously easy question, that means I got the last question wrong.

First of all, a question that seems easy to you may or may not actually be a truly "easy" question, that is, one that most people get right.  Even if it is, no conclusion can be drawn about the previous question.  The CAT is running a complex algorithm, which sometimes involves giving you a very easy or a very hard question.  Don't take it personally: the computer is just running its algorithm.


Fact: You can get several questions wrong and still get a good score.

The CAT has to give you several questions well above your ability, questions that you almost invariably will get wrong, in order for it to zero in on your actual ability.  You are not penalized for that: that's just what the CAT must do as part of its algorithm.


Myth: The first question is super-important, because that determines the course of easy/hard questions from there.

Totally false.  The CAT is performing a complex process of estimation that can handle aberrations, even if one of the aberrations happens on question #1.  Don’t worry: over the course of the whole test, the computer will give you the combination of questions it must in order to determine your abilities.  Furthermore, the algorithm is such that order of the questions doesn't affect your score at all.  If you get a certain question right then whether it was the first question, a middle question, or the last question, doesn't matter at all.  What does matter for your score is the difficulty of the question, and whether you got it right or wrong, but not where it fell in the test.


Fact: Not finishing all the questions in a section hurts your score.

That is quite true.  It's exceedingly important not only to learn content and strategy, but all practice at working efficiently, so that you don't run out of time.  Ideally, you want to hone your time management skills so that you have abundant time on even the last questions on a section.


Myth: You can outthink the CAT.

The algorithm is far too complex.  There's no sense stressing about "how did I do on those question?" or "why is it asking this kind of question now?"  Just do your best on the question in front of you at any moment, submit it, and then forget about that question entirely.


Fact: Systematically reviewing math and verbal content, as well as strategies specific to each question type, can vastly enhance your GMAT score.

That is most certainly true, and that's why Magoosh can give you such an advantage.  With a couple hundred lesson videos discussing both content and strategy, and over 800 practice questions, each with its own video explanation, you will get top-notch preparation for the GMAT at only a fraction of what you would pay for a comparable course.
This post was written by Mike McGarry, GMAT Expert at Magoosh GMAT, and originally posted here.

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