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# GMAT Scoring Algorithm - My observations

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08 May 2006, 23:21
Analysis-1

At present I have 4 Data Point, Following is obvious observation about type/number of questions asked.

For Quant
DS - 18-19
PS - 18-19

For Verbal
SC: 16
CR: 11
RC: 14

4 Data are not statistically enough to conclude anything regarding scoring!

Please help out by filling this file to generate more data. Once I have around 10 Data I will update file for everyoneâ€™s analysis.

I have updated score report file to accommodate not attempted questions.
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08 May 2006, 23:47
willget800 wrote:
Good job of analysis there.. But I am not sure how to define the middle section..

Also I am assuming you forming this strategy only for Verbal? Or do you expect the same is used for Quant too?

I would loosely define middle section as 15 to 35 for V and 15 to 32 for Q,

I would say for quant also analysis should be applicable.

Specifically I have read in many briefing that they were getting very hard questions initially but still they were able to finish as later on as question were becoming easy.

I think these phenomena may be due to two reasons

A) Algorithm has adapted to your level from initial questions, and now itâ€™s trying to fine tune your exact level so itâ€™s not really giving very hard questions.
B) Some of experimental question might be on easier side for oneâ€™s caliber so he can easily answer it (off course some will be tougher too)

Remember algorithm needs to statistically prove that question is of particular difficulty level. Letâ€™s say, if question is of 650 level, according to test maker, they may try to throw this question to persons whose level is between 600-700, and if 600 levels candidate are answering it incorrectly and 700 level candidate is answering it correctly they know that question is between 600 to 700 level.

More over if a personâ€™s caliber is really 750 but due to some initial mishaps (answering few easy incorrectly) if software thinks he is of 650 level than most of experimental question, which are 600-700 level, will be very easy for candidate and he may be able to breeze through them finishing test promptly.
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08 May 2006, 23:52
OasisNYK wrote:
Well the bottom line is we may never know the truth about how the GMAT is truly scored - but this seems to be a great theory.

As with most of sports, with GMAT you will never exactly know what your opponent thinks but still you need to strategize for various tricks he is going to use against you. Itâ€™ll always pay off to know the rules of game by heart and you are really better off if you know rules which your opponent followsâ€¦
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11 May 2006, 04:12
As for me,
I think that at least first 15 questions are important.
GMATPrep 1, Verbal part, mistakes in first 15 - 2 (Total mistakes 11), Score - 37.
GMATPrep 2, Verbal part, mistakes in first 15 - 6 (Total mistakes 12), Score - 32.
Chiragr, I will send you your table shortly.
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02 Jun 2006, 21:59
2
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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.

http://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: http://img485.imageshack.us/img485/9021/j225a338sk.jpg

But then we end up here: http://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:

http://img140.imageshack.us/img140/3223/j471a233yx.jpg

But how does it decide what to show me?

http://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:

http://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:

http://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.
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14 Jun 2006, 04:35
Dear rhyme..
I m engineer. I believe that your analysis is very sound and supported by very good examples and theory.

Keep on with the good work. I second you in this matter and would admit that reasoning you have given is well supporting

ANKUSH
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14 Jun 2006, 07:56
Great post rhyme. My advise is try to manage your time well so that you can complete the entire section without having to rush the last few questions. This way you would give the fullest information to the test engine to assess your true ability. If you don't finish the last few questions it is likely that the test engine has not got enough opportunities to narrow the range down to your ability score and thus you could be penalized.

Also, regarding experimental questions. A question being experimental means that it has not been assigned an ability level yet. In other words there would not be a decision to make so that the high achievers get the "high ability experimental questions" and vise versa. An experimental question has to be tested randomly over the entire range of the test because when it becomes a real question it would have to be ready to be used anywhere in the test. Level of a question would be assigned based on what percentage of the entire testing population can answer the specific question correctly.

The final point is, there is no use to try to guess if a question is experimental or not. It will not do you any good. Just try to answer each question as best as you could, within reasonable time. Not to spend too much time in the beginning or any of the questions, nor to rush in the end, this is the best strategy. Remember, the purpose of GMAT is not to trick you or cheat you, it is to try to assess your true ability.

To really understand how GMAT test engine work, I suggest you to study item response theory.
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20 Jun 2006, 06:15
The technique at which the GMAT test engine is based is called item response theroy.

IRT relates characteristics of items (item parameters) and characteristics of individuals (latent traits) to the probability of a positive response. A variety of IRT models have been developed for dichotomous and polytomous data. In each case, the probability of answering correctly or endorsing a particular response category can be represented graphically by an item (option) response function (IRF/ORF). These functions represent the nonlinear regression of a response probability on a latent trait, such as conscientiousness or verbal ability (Hulin, Drasgow, & Parsons, 1983).

In laymen's term, each test question has a response curve, showing the probability of answering it correctly for each person with certain level of latent ability. Items/questions can be selected that provide the most information for each examinee so that in the end of the test the true ability score of each examinee can be estimated with reasonable accuracy. IRT allow researchers to calculate conditional standard errors of measurement based on a test information function, rather than assuming an average standard error across all trait levels. This allows researchers to select items that provide maximum measurement precision in a particular ability/trait range.

When 41 questions or whatever questions were selected to construct the test, it is determined that these questions will provide the best information for a person's ability. If you adopt certain "strategy" to "beat" or "game" the test engine, by focusing on a portion of the questions and neglect the others, you should know that you have not allowed the test engine to obtain the fullest information about you, and thus its estimate of your ability may become inacurate. It will be very difficult to manipulate the inacuracy so that it is to your favor.

In other words, I would highly encourage everybody to concentrate their effort to level up their true ability, instead of spending time trying to "game" the test engine.
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20 Jun 2006, 06:43
Sounds good ...
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20 Jun 2006, 10:57
I have a bit different view on this, seeing my practice scores. One thing is sure, the algorithm is probably not easy to analyze or think, since there is absolutely no way to see how many questions you answered wrong & why your score is low or high....bottom line is: FORGET ABOUT ALGORITHM, JUST CONCENTRATE ON GETTING EACH & EVERY QUESTION CORRECT!!! The more you think about the algorithm, the more you waste your time.
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20 Jun 2006, 16:02
Question 1 = raw ability score = X + or - 5Y, probability of getting it right, 0.5, answered correctly
Question 2 = raw ability score = X + or - 4.5Y, probability of getting it right, 0.4, answered correctly
Question 3 = raw ability score = X + or - 4.48Y, probability of getting it right, 0.3, answered incorrectly
Question 4 = raw ability score = X + or - 4.45Y, probability of correct 0.6, answered correctly...

Question 41 = Raw ability score = X + or - 0.005Y

Bands converge.

Raw ability is found.

No question is worth more than the other. (The world largest myth)
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18 Jul 2006, 23:56
By now everyone has probably already heard this, but Stanford will now accept that GRE and the GMAT for its MBA program. It appears that theETS is back in the MBA admissions market. Frankly, I think this is a good thing- the GRE is at least as well constructed as the GMAT,is administered to a large number of takers each year, and is cheaper. It is also good in that it breaks the monopoly of the GMAT- if undergrad has two admissions tests, it makes sense to allow MBA applicants to choose which test to submit.
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31 Jul 2006, 17:33
I think the strategy on how to handle the first part of the test depends on the skill of the test-taker.

It has been suggested that someone shoot for 800 (or a really high score) will need to make time to handle every question thrown at him. In fact, a key to getting a high score is probably working quickly and efficiently through very difficult questions.

On the other hand, I do think that it makes sense for someone shooting for a lower number, say 600-650 to spend much more time on the early part of the test. The reason is not because I believe they early questions are more or less important, but because it's more likely that someone scoring at this level will benefit from the increased time spent on these questions.

If someone is scoring at the 600 level, for example, it's unlikely that they will be successful with a 750 level question shown to them later in the test, even if they have enough to to deal with it. So, trying to gain the extra time by speeding through the early part of the test does not make sense for this type of test taker. It would be better to spend the time on questions where they have a legitimate shot of coming up with the right answer.

On the other hand, someone shooting for a 750 will probably have to plan to work quickly throughout the entire test, including the beginning and end of each section. A very high score can only be achieved if the test taker leaves enough time to make a legitimate attempt at almost every single question.

So, regarding the advice by Kaplan and PR, I think that they are addressing their largest constituency when they advise people to concentrate on the early questions. a 700 score is up over the 90th percentile, and a 750 is over 99th. These are the types of test takes that know what they must do going in, and do not need test-taking advice; but they constitute less than 10% of the test-taking population. Kaplan and PR make their money by teaching skills to the bulk of the people.
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05 Aug 2006, 17:24
I believe you are right. Definitely, the first few questions are the most important. Let's put it this way - you end up with a higher score with the same number of questions right, if the mistakes occur at the end. I also, believe that if the questions that you get wrong belong to the same category - say geometric interpretations, then you score tends to be lower.

As far as verbal goes, I get the feeling that if you get a reading comprehension too early, it means you are doing well.
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26 Aug 2006, 08:59
A few MBA programs beyond Stanford accept the GRE. One could not describe this as a flood, but it does appear that the use of the GRE is spreading.

For example, Williamette in Oregon accepts both the GMAT and the GRE
http://www.willamette.edu/agsm/full-time/faq/#6

University of Washington Tacoma (GRE accepted but GMAT preferred)
http://www.tacoma.washington.edu:82/pro ... _GMAT.html

University of Wisconsin Eau Claire

University of North Texas
http://www.coba.unt.edu/programs/masters/info.php#gmat

University of Dallas

University of Minnesota Duluth
http://www.d.umn.edu/lsbe/mba/mba_gmat.php
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04 Dec 2006, 22:02
Hjort wrote:
Has anyone else tried this formula?

Worked for me perfectly. Q46,V42 = 710

Cheers. L.
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12 Dec 2006, 09:38
Yep! 46V, 41Q = 709.75 (710 from the folks at GMAC).
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17 Aug 2007, 17:58
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Please read this before asking "How many questions can I get wrong before I get a X score on the GMAT" or "is the first 10 questions more important than the later ones?"

our illustrious rhyme has written this dissertation on the algorithms. Based on the little I know, I think he's got it on the spot. So read on and just focus your test time on doing your best, double checking your answers, and moving on. Any second-guessing the system will only hurt you instead of help you.

Kryzak

Quote:
This is a fundamental misunderstanding to how adaptive tests work.

The first few questions do not count more than the last few.

The number you get wrong is meaningless. You could get 15 wrong and score 700, it wouldn't matter (there will be some upper limit .. at some point you have to get something right to score well)

Its WHICH questions you get wrong that matter.

I wish I could find my post from ages ago that describes how this works in detail, unfortunately I can't.

Oh wait... here it is...

The super short version: There is a bell curve. The system figures out where you sit on it. In 37 questions, you can't "fool it".

The longer version: Here it is in a nutshell.. The GMAT develops a confidence interval around your score. In the beginning this score is wide - say, 500 to 600, as you answer questions, two things happen - one, it tightens the band (550 to 575 say) and it changes the actual estimate (say 571). (Think raw scores if you want) Eventually it tries to get to a point where the probability of getting a question right is .5 - that is your "estimated ability" is precisely in the middle of a standard normal curve, and around that is a very narrow band - a confidence interval of your score (the variance decreases, think basic stats.. Few numbers with large ranges vs lots of data points with trending singularity - variance decreases over time with each q answered).

The bottom line is this: whether or not you get the first question right or wrong doesn't matter because by the time you get to 37, it will have "snuffed" you out. Moreover, how many questions you get right doesn't matter either (again, within reason, if you get all 37 wrong then yea, it matters) - its WHICH questions you get right. This is the critical thing to remember - its not whether or not you get one right ... its whether or not you got one with P < .5 right. Getting a "600" level question right (where for you p(correct) = .5)) is not the same as getting a "700" level question right.

Put it this way. I could get every single question at 600 right and NEVER get a 700 question right. No matter whether I end up getting 20 questions right and 10 700 questions wrong, my score isn't going to get to 700. Similarly, I could get 29 questions right, and 1 question wrong - if that question I got wrong was a 700 score question, I'm not getting a 700.

Make sense? Think about a bell curve that keeps getting tighter... So where was I ? Oh yea... Moreover, the software is using a bell curve, not a retarded monkey, to figure out your score. So getting one wrong doesn't decrease your score by 20 points and getting one right increase it by 20. If it did, it would be very very easy to figure out your score (see later how Kaplan and others make this insanely stupid assumption in their materials). What happens of course is that it takes an amalgamation of data points to determine the move in your score - your previous responses, the level of difficulty of that particular question, the confidence interval and variance expected around your "True" ability, the probability estimate for your true ability at a given question etc... All of this helps it decide how far to move your score up and down....

But the key to realize here - and this is the key - is that the band of scores you get continues to get TIGHTER AND TIGHTER with every question - while it keeps shifting up and down trying to gather data. Fundamentally, after 37 questions its shifted a bunch and the band has become narrow. Whether or not you got the first question right or wrong really doesnt matter.

Now for more detail:

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.

http://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: http://img485.imageshack.us/img485/9021/j225a338sk.jpg

But then we end up here: http://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:

http://img140.imageshack.us/img140/3223/j471a233yx.jpg

But how does it decide what to show me?

http://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:

http://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:

http://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 Oops 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.
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31 Aug 2007, 01:39
Thanks. Interesting post.

However, for the sake of PRACTICING, I would really want to know, ow many WRONG ANSWERS are allowed if I am targeting 700, for example?

I wonder how people could tell they scored V43 Q47, blah blah...

What I knew from trial tests (paper based) was, for example, I got 31/37 right answers for Quant, 31/41 right answers for Verbal.

How should I estimate my "level"?
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12 Oct 2007, 10:07
I dont think we can determine how many correct answers need to be got to get 700. As mentioned in the earlier post, each question has its own importance to determine the score and even after getting 10 questions wrong, one can still end up with 750

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# GMAT Scoring Algorithm - My observations

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