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Many observers have criticized the difficulty of the questions that appear in the OG (the Official Guide). The problem is not so much that the OG items are too easy as it is that the OG, like a traditional pencil and paper test, features items that range across the p scale. The high probability items (the easy questions) are generally of little interest to students who are seeking scaled scores at the far right tail. Suppose we group items into seven difficulty strata with the middle stratum called stratum x. The majority of items that one would encounter on a traditional pencil and paper test would come from the middle strata near x (i.e. x-1, x, x+1). In a traditional test, you would encounter very few questions at the top of the range (x+3) since these questions have undesirable characteristics for most test takers (it would provide low differentiation (discrimination) among low and medium ability test takers).
Now suppose we create an adaptive test from this body of traditional questions. The first test item administered to each student would come from the middle stratum (stratum x). If it is answered correctly, we move to stratum x+1 for the second question. If the first question is answered incorrectly, we move to stratum x-1 for the second question. If the first two questions are both correct, we move to stratum x+2. If this questions is answered incorrectly, we move back down to stratum x+1. At the end of the test we would combine the information concerning difficulty and number of questions answered correctly and incorrectly to obtain an estimate of the net number of items this student would have answered correctly on a traditional paper based test (this is the raw score). The estimated raw score on the paper test is then used to read the associated scaled score from the paper test's raw to scaled score conversion table.
Hjort
Now suppose we create an adaptive test from this body of traditional questions. The first test item administered to each student would come from the middle stratum (stratum x). If it is answered correctly, we move to stratum x+1 for the second question. If the first question is answered incorrectly, we move to stratum x-1 for the second question. If the first two questions are both correct, we move to stratum x+2. If this questions is answered incorrectly, we move back down to stratum x+1. At the end of the test we would combine the information concerning difficulty and number of questions answered correctly and incorrectly to obtain an estimate of the net number of items this student would have answered correctly on a traditional paper based test (this is the raw score). The estimated raw score on the paper test is then used to read the associated scaled score from the paper test's raw to scaled score conversion table.
Hjort
11 Nov 2004, 10:43
Kudos
Bookmarks
There is a common argument that the GMAT is irrelevant to MBA admissions since schools can use so many other admissions factors in making their choices.
It is crucial to remember, however, that the GMAT has far more predictive power than most other admissions criteria. For instance, the median correlation of V,Q,andAWA scores with first year MBA grades was .42 while the median correlation of undergrad grades with first year MBA was only .25. When the GMAT and undergrad grades are combined the correlation increases to 0.47. Thus, assertions by schools that they weigh all admissions factors equally should be viewed skeptically (of course the correlation varies from school to school).
The median correlation for undergrad GPA and first year MBA is 0.25 as corrected above.
Hjort
It is crucial to remember, however, that the GMAT has far more predictive power than most other admissions criteria. For instance, the median correlation of V,Q,andAWA scores with first year MBA grades was .42 while the median correlation of undergrad grades with first year MBA was only .25. When the GMAT and undergrad grades are combined the correlation increases to 0.47. Thus, assertions by schools that they weigh all admissions factors equally should be viewed skeptically (of course the correlation varies from school to school).
The median correlation for undergrad GPA and first year MBA is 0.25 as corrected above.
Hjort
02 Jun 2006, 21:59
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Frankly,
I'm surprised no one sees the problem with this - knowing which questions you got right and which questions you got wrong tells you nothing. Each question has an assigned difficulty based on a statistical likelyhood of you getting it right on based on the computers estimate of your true ability. This difficulty isn't based on an "easy" or "hard" setting, its a probability of getting the question correct.
Imagine each question with a bell curve of correct answers based on your true ability level. That is, each question has a known difficulty level. There is an expected number of right answers for people with true ability level of X and a percent of expected correct answers at Y.
I'm going to steal graphs from another site to make the point.
https://img485.imageshack.us/img485/5043/j225a322tn.jpg
In this graph, based on my previous response, the probability of getting this right is roughly 80% at this particular skill level. Ignore the bottom numers OK? Those aren't supposed to be a gmat score specifically. Think of "500" as ability level 3. Maybe a 600 is ability level 3.42.
As I answer a question the system figures out my "true" ability level estimate. This is based on the bell curves of the questions I got right and the inverse of the questions I got wrong.
So, lets say my true ability level is "4.0", an the GMAT ranks ability levels from 0 to 5. It'll hand me an ability level question of 2.5 to start, to guage my true ability.
At this point, the GMAT will do a few things:
1) It will update my ability estimate based on my answer.
2) It will determine the confidence interval for this ability estimate
So maybe we start out here: https://img485.imageshack.us/img485/9021/j225a338sk.jpg
But then we end up here: https://img140.imageshack.us/img140/9544/j471a135cp.jpg
The black line is my current estimated ability, the red my true ability and the yellow banded area is a confidence
interval.
As I answer questions, the estimated ability level comes towards the true level:
https://img140.imageshack.us/img140/3223/j471a233yx.jpg
But how does it decide what to show me?
https://img140.imageshack.us/img140/3191/j471a219dn.jpg
As I answer questions, the software uses its current estimate of your score by evaluating questions avaliable around that band and selects the one most appropriate.
As we keep doing this the confidence interval will continue to move - tighter and tighter.
Until eventually, the interval decreases:
https://img140.imageshack.us/img140/5456/j471a738yb.jpg
This is basically how the GMAT works, though from what I understand it comes to it's true ability estimate by meshing the curves as well, so the intervals get very small by the 37th question.
This doesnt mean the first questions are worth more... it means you are more likely to get an overly difficult or overly easy problem in the first ten questions because the band in which - the confidence interval of questions to pick from - is still wide... but the way it changes its own estimates will depend on the questions you get but they do NOT impact your score more than other questions.
The reason people seem to think this is because they sway more, so if you get a really easy one wrong early on, it might give you a really really question and set your ability level low, but this is only temporary as BY DEFINITION, the exam's purpose is to narrow that band to your natural ability.
By definition the exam is going to continue to give you questions to get your probability level to .5 on each question - this will give a nice confidence band and a good indication of you true ability.
Kaplan and Princeton all argue the first few questions argue more. The whole premise of their argument lies in the ridiculously simplified concept of a graph that looks like this:
https://img149.imageshack.us/img149/5439 ... ive1uh.gif
This, however makes NO SENSE. The sap getting hard questions right would quickly see his score increase, yes, but would very quickly hit a probability of .5, in which case he would flatten out. The person who saw their score decrease, would, of course get an easier question on #2, but based on their true ability, they would also be increased on subsequent correction questions - each question modifies the software's estimate of your true ability. The probabiliy of getting an easier question goes up, but so does the p that it is answered correctly..
In fact, if you really want to get into it....
One can just as equally argue that, in the begining the software is wildly guessing - and lets say that you just get lucky and get 5 really damn hard questions right. The software has 32 more questions to find your true ability. It will. If on the other hand, you END WITH 5 extremely hard questions that you get right, the software may have found your true ability by question 32 - in which the 5 you randomly got correct by luck, have increased your overall score. Woot!
But do you see it? It goes the other way too...
Lets say you get hte first 10 right. The machine thinks you are a 750er. You think it wont adjust that by the time you get to question 37? Now think. What happens if you get the first 10 right, and the last 10 wrong? By then, its narrowed your estimated ability yes, but with each incorrect answer (after the first), you begin to widen that band again - and the software will readjust your true ability estimate downwards. The confidence levels will remain tight but your overall score has still decreased just as if you ahd taken the first 10 and gotten them wrong.
The only difference here is whether the questions sets become exhausted or less than ideal at a given level - unlikely as hell on the gmat - but even if the software is forced to give you less than p=.5 q's, it would still effectively continue to drop your score approriately - and proportionally.
In other words,
Question 1 is just as important as question 37.
----------------
As for the attempt to figure out where the experimentals are... your logic is flawed. You are thinking of each question as being a question of "X difficulty", like a "700 question", its not like that - each question has a probability associated with a given skill level.
So for a certain problem, you might have something like:
500 | 510 | 520 | 530 ...... | 750 | 760 | 770
0.1 0.12 0.3 0.31 | 0.51 | 0.6 | 0.7
That is, the higher your true ability, the higher the probability you get it right...
Experimentals can show up anywhere. The only exception I would expect would be question 1.
I'm surprised no one sees the problem with this - knowing which questions you got right and which questions you got wrong tells you nothing. Each question has an assigned difficulty based on a statistical likelyhood of you getting it right on based on the computers estimate of your true ability. This difficulty isn't based on an "easy" or "hard" setting, its a probability of getting the question correct.
Imagine each question with a bell curve of correct answers based on your true ability level. That is, each question has a known difficulty level. There is an expected number of right answers for people with true ability level of X and a percent of expected correct answers at Y.
I'm going to steal graphs from another site to make the point.
https://img485.imageshack.us/img485/5043/j225a322tn.jpg
In this graph, based on my previous response, the probability of getting this right is roughly 80% at this particular skill level. Ignore the bottom numers OK? Those aren't supposed to be a gmat score specifically. Think of "500" as ability level 3. Maybe a 600 is ability level 3.42.
As I answer a question the system figures out my "true" ability level estimate. This is based on the bell curves of the questions I got right and the inverse of the questions I got wrong.
So, lets say my true ability level is "4.0", an the GMAT ranks ability levels from 0 to 5. It'll hand me an ability level question of 2.5 to start, to guage my true ability.
At this point, the GMAT will do a few things:
1) It will update my ability estimate based on my answer.
2) It will determine the confidence interval for this ability estimate
So maybe we start out here: https://img485.imageshack.us/img485/9021/j225a338sk.jpg
But then we end up here: https://img140.imageshack.us/img140/9544/j471a135cp.jpg
The black line is my current estimated ability, the red my true ability and the yellow banded area is a confidence
interval.
As I answer questions, the estimated ability level comes towards the true level:
https://img140.imageshack.us/img140/3223/j471a233yx.jpg
But how does it decide what to show me?
https://img140.imageshack.us/img140/3191/j471a219dn.jpg
As I answer questions, the software uses its current estimate of your score by evaluating questions avaliable around that band and selects the one most appropriate.
As we keep doing this the confidence interval will continue to move - tighter and tighter.
Until eventually, the interval decreases:
https://img140.imageshack.us/img140/5456/j471a738yb.jpg
This is basically how the GMAT works, though from what I understand it comes to it's true ability estimate by meshing the curves as well, so the intervals get very small by the 37th question.
This doesnt mean the first questions are worth more... it means you are more likely to get an overly difficult or overly easy problem in the first ten questions because the band in which - the confidence interval of questions to pick from - is still wide... but the way it changes its own estimates will depend on the questions you get but they do NOT impact your score more than other questions.
The reason people seem to think this is because they sway more, so if you get a really easy one wrong early on, it might give you a really really question and set your ability level low, but this is only temporary as BY DEFINITION, the exam's purpose is to narrow that band to your natural ability.
By definition the exam is going to continue to give you questions to get your probability level to .5 on each question - this will give a nice confidence band and a good indication of you true ability.
Kaplan and Princeton all argue the first few questions argue more. The whole premise of their argument lies in the ridiculously simplified concept of a graph that looks like this:
https://img149.imageshack.us/img149/5439 ... ive1uh.gif
This, however makes NO SENSE. The sap getting hard questions right would quickly see his score increase, yes, but would very quickly hit a probability of .5, in which case he would flatten out. The person who saw their score decrease, would, of course get an easier question on #2, but based on their true ability, they would also be increased on subsequent correction questions - each question modifies the software's estimate of your true ability. The probabiliy of getting an easier question goes up, but so does the p that it is answered correctly..
In fact, if you really want to get into it....
One can just as equally argue that, in the begining the software is wildly guessing - and lets say that you just get lucky and get 5 really damn hard questions right. The software has 32 more questions to find your true ability. It will. If on the other hand, you END WITH 5 extremely hard questions that you get right, the software may have found your true ability by question 32 - in which the 5 you randomly got correct by luck, have increased your overall score. Woot!
But do you see it? It goes the other way too...
Lets say you get hte first 10 right. The machine thinks you are a 750er. You think it wont adjust that by the time you get to question 37? Now think. What happens if you get the first 10 right, and the last 10 wrong? By then, its narrowed your estimated ability yes, but with each incorrect answer (after the first), you begin to widen that band again - and the software will readjust your true ability estimate downwards. The confidence levels will remain tight but your overall score has still decreased just as if you ahd taken the first 10 and gotten them wrong.
The only difference here is whether the questions sets become exhausted or less than ideal at a given level - unlikely as hell on the gmat - but even if the software is forced to give you less than p=.5 q's, it would still effectively continue to drop your score approriately - and proportionally.
In other words,
Question 1 is just as important as question 37.
----------------
As for the attempt to figure out where the experimentals are... your logic is flawed. You are thinking of each question as being a question of "X difficulty", like a "700 question", its not like that - each question has a probability associated with a given skill level.
So for a certain problem, you might have something like:
500 | 510 | 520 | 530 ...... | 750 | 760 | 770
0.1 0.12 0.3 0.31 | 0.51 | 0.6 | 0.7
That is, the higher your true ability, the higher the probability you get it right...
Experimentals can show up anywhere. The only exception I would expect would be question 1.
)
. However, I do not have any insights into it yet. Maybe soon enough... 
