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Background:

I read this article on "hackaday" about alleged "large-scale cheating" on the ISC exam. It gives this as source.

Here is one of the images from the site:

enter image description here

The hack-a-day asks for speculation about the nature of the "cheating" that the data indicates.

My challenge is: determine the actual (non-cheat) distribution from this tampered result and justify your answer with strong and appropriate use of statistics.

EngrStudent
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  • Perhaps the marking scheme and examination questions are available somewhere. There may be some mix of right or wrong questions and some tougher ones. There may be a protocol to round reported marks for some reason; otherwise why so many even marks? But it seems strange that in an exam taken by thousands of students there are apparently no students below about 13%. There is usually someone who panics or feels sick, etc. and the very weakest students would just get right answers on a few simple questions. – Nick Cox Jun 06 '13 at 18:26
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    A recent sample examination is available at http://cisce.org/data/Specimen%20Question%20Paper/SPE%20QPS%202011/13.%20Mathematics.pdf. Apparently eight ten-point questions are graded (and given partial credit): to convert from 80 points to a 100 point scale, some rescaling and rounding are necessary. For a responsible analysis, though (in place of the overblown accusations of "cheating" in the references), it is important to know how the grading was done, how it was reduced to this 0-100 scale, and what the critical passing scores are. – whuber Jun 06 '13 at 19:40
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    There's a bunch of ways patterns like that might occur. I wouldn't leap straight to 'cheating'. I wonder if they noticed the spelling mistake in the graph... and why is the y-axis labelled 'strength'? Strength of what? – Glen_b Jun 07 '13 at 03:56
  • link At some point there was a bit of cheating, but this is likely not it. – EngrStudent Dec 18 '15 at 18:14

1 Answers1

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Maybe there has been no cheating?

Here's a (incomplete) data generation proposal:

Imagine the exam has 99/100 questions worth 2 points, and 1 really difficult question with 1 point. The smartest students, near the right tail, will probably get the hard question, and have some variation in the other 99 questions. This might explain the right tail's smoothness.

Cam.Davidson.Pilon
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  • but the blogger, who has more than a visual, says: For example, 81, 82, 84, 85, 87, 89, 91 and 93 were visibly missing., so my suggestion is ruled out. – Cam.Davidson.Pilon Jun 06 '13 at 19:26
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    If you look at whubers comment, his idea can lend credibility to yours. If they are 10 points each then maybe this is an artifact of rounding policies. – EngrStudent Jun 06 '13 at 19:49