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Math tasks ordered by difficulty level for GMAT / GRE / SAT

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New post 19 Jul 2017, 09:23
Hello everybody

For a research project (study) I'm searching math tasks ordered by difficulty (easy to hard) and average time needed to solve. I think and I hope that there is also some ordering according to difficulty level in the GMAT / GRE / SAT tests. I would prefer if the difficulty level is inferred from the analysis of the performance of participants instead of the estimation of a single person (but latter would also be acceptable).

Does somebody know a resource which provides such an ordering of difficulty level and perhaps also the average time to solve for the tasks?
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New post 19 Jul 2017, 09:35
You can use the GMAT Club Timer stats and gather a lot of stats question by question : https://gmatclub.com/forum/the-three-si ... 20970.html
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New post 19 Jul 2017, 09:50
I don't think that information exists in any precise form. Some GMAT resources (the add-on question pack in GMATPrep, for example) will give an official classification of questions, Easy, Medium or Hard, and that classification will certainly have been inferred from test taker performance on those questions, since that's how these tests work. But if you're looking for the b-value (difficulty level), in IRT terms, for a pool of GMAT questions, that's not published information, and if you want to generate that information yourself, you'd need responses from hundreds of test takers, along with the ability level of each test taker, to estimate b-values accurately. GMAT questions will have been designed with the two-minute average time limit in mind, but you won't find any official information about the time test takers spend on individual questions.

There is data that you might somehow be able to use, though there are enormous sample bias issues that could make the data unreliable. If you look at a random GMAT math question posted on this forum, (say here: https://gmatclub.com/forum/if-it-is-tru ... -9602.html ) and you open the 'show timer statistics' panel, you'll see a breakdown of responses from forum participants, along with how long they took to arrive at right or wrong answers. I don't know anything about how those stats are compiled, nor anything about the people who submit answers there, but it might be the only data of that kind you can get. (edit - bb pointed that out while I was writing my post!)
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New post 19 Jul 2017, 13:55
Thank you very much for your answers. I appreciate it.

I'm exactly looking for the b-value in IRT term as you said. The statistics of the math questions of this forum looks interesting. Is there also a sorted list of math tasks available (by category and difficulty)? Or perhaps as a database? Why is there an enormous sample bias?

Do you know if there is an average time limit for SAT, ACT and GRE like the two-minute limit for GMAT?

By the way, if there is a pool of data available for GMAT, GRE, SAT or ACT I could calculate the difficulty level by myself using IRT.
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New post 19 Jul 2017, 14:50
There are several potential sources of bias. The participants on this forum aren't likely to be a representative random sample of test takers in general, for one thing - for example, anyone here has to have a certain level of commitment to their preparation that not all test takers have. And when you look at individual questions posted here, it's not the case that every forum member answers every question. I have no idea who does answer the questions, but the questions are flagged with an estimated difficulty level, and I'd imagine it's possible that higher level test takers often don't bother attempting easy questions, and that lower level test takers often don't bother attempting harder questions. And since there are no consequences for a wrong answer, some people possibly aren't treating questions here as seriously as they would if the question were on a test.

I've never seen any officially published data on test questions from any of the major tests; as far as I know, that information has always been kept confidential. I did see an IRT research paper from several years ago, and the authors of that paper had used a batch of real GMAT questions, along with the relevant item statistics, which I think they had acquired directly from the test developer, but I'd have to go back to the paper to confirm.

It's been a long time since I've looked at either the SAT or ACT tests. The GRE is a faster test than the GMAT, about 90 seconds per Quant question, but the questions are also more straightforward.

Can you share any details about the research you're conducting?
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Re: Math tasks ordered by difficulty level for GMAT / GRE / SAT   [#permalink] 19 Jul 2017, 14:50
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