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22 May 2014, 08:06
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If you get every question right in a section, will you automatically get a 51 scaled score?
I ask because on the 2nd GMATPrep test, I missed one question in the Verbal section and got a 48. Would that one question have bumped me up to a 51? (I know it's not quite that simple since I may have seen different questions as a result of the miss, but humor me)
I ask because on the 2nd GMATPrep test, I missed one question in the Verbal section and got a 48. Would that one question have bumped me up to a 51? (I know it's not quite that simple since I may have seen different questions as a result of the miss, but humor me)
22 May 2014, 11:20
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GMAT scoring is really interesting on the back end, so thanks for the question and the opportunity to discuss it!
The way your score is calculated, the Item Response Theory system uses a "theta estimate" to score your performance, and then maps that number (which you'll never see but it essentially acts as a percentile, comparing your ability with that of all other test takers) to a scaled score, and *then* takes that scaled score and reports the percentile.
On the verbal section, the scaled score marks of 46-51 are all "99th percentile" which means there's just not very much differentiation between those individual scores. So that's why really minor changes in theta estimate might cause a pretty significant jump in scaled score - the way that the scaled scores map to percentiles, there are almost too many scaled scores for such a small percentage of test-takers.
One thing that this brings up that people ask about all the time - your score out of 800 is determined by your theta scores, not your scaled scores. Which is why someone with the same split as you (say, 49Q, 42V) might have an overall score that's 10 points lower than yours (which would be because your thetas fell at the "high end" of the 49/42 ranges and they just squeaked into the 49/42 areas).
As far as your overall question...there shouldn't ever be a case on the official test in which you get every question right and don't get the max scaled score. The official pool of questions will have enough "high difficulty" questions that if you've answered them all correctly the system shouldn't have any reason to doubt your ability. Theta scores essentially function as probabilities - "based on your performance on these questions, for which ability theta do you have the highest probability?". As long as you've been presented with the opportunity to answer several questions at that extremely high difficulty threshold, and you've answered everything correctly, the system should report the highest probability as being the max theta (3.0) because there's no evidence to the contrary and there's plenty of evidence supporting that you have that max ability. I guess theoretically if you hadn't been presented with enough challenging questions to give the system enough confidence in that max probability, you could end up a little to the left of that, but as long as the pool of questions is deep enough to provide you with those opportunities - and the official GMAT's pool is plenty deep - you'd hit the max.
I hope that helps...and sorry to geek out a little too much on IRT!
The way your score is calculated, the Item Response Theory system uses a "theta estimate" to score your performance, and then maps that number (which you'll never see but it essentially acts as a percentile, comparing your ability with that of all other test takers) to a scaled score, and *then* takes that scaled score and reports the percentile.
On the verbal section, the scaled score marks of 46-51 are all "99th percentile" which means there's just not very much differentiation between those individual scores. So that's why really minor changes in theta estimate might cause a pretty significant jump in scaled score - the way that the scaled scores map to percentiles, there are almost too many scaled scores for such a small percentage of test-takers.
One thing that this brings up that people ask about all the time - your score out of 800 is determined by your theta scores, not your scaled scores. Which is why someone with the same split as you (say, 49Q, 42V) might have an overall score that's 10 points lower than yours (which would be because your thetas fell at the "high end" of the 49/42 ranges and they just squeaked into the 49/42 areas).
As far as your overall question...there shouldn't ever be a case on the official test in which you get every question right and don't get the max scaled score. The official pool of questions will have enough "high difficulty" questions that if you've answered them all correctly the system shouldn't have any reason to doubt your ability. Theta scores essentially function as probabilities - "based on your performance on these questions, for which ability theta do you have the highest probability?". As long as you've been presented with the opportunity to answer several questions at that extremely high difficulty threshold, and you've answered everything correctly, the system should report the highest probability as being the max theta (3.0) because there's no evidence to the contrary and there's plenty of evidence supporting that you have that max ability. I guess theoretically if you hadn't been presented with enough challenging questions to give the system enough confidence in that max probability, you could end up a little to the left of that, but as long as the pool of questions is deep enough to provide you with those opportunities - and the official GMAT's pool is plenty deep - you'd hit the max.
I hope that helps...and sorry to geek out a little too much on IRT!
