Probability Question for David Sklansky

[Borodog]

Others are welcome as well, but David is the master of these sorts of problems, so I'd like to hear his response.

Two of my students missed Test 4 and had to take a makeup. They took the test at the same time, in the same room, sitting at the same table. The test on the left is the male's, the test on the right the female's. He got 14/19, she 15/19. His previous test scores are significantly better than hers. In case you can't tell from the picture, on her test, on number 11 she had originally selected D, but then erased it and chose C. The girl is of above average attractiveness.

What is the probability that cheating occurred?

[vhawk01]

Wouldn't he need to know some estimate of the likelihood of each person getting any given question correctly? You could easily craft a test where this was 100:1 and a near lock to be cheating.

[DougShrapnel]

Zero, but I'd estimate that teamwork occured 1. [img]/images/graemlins/smile.gif[/img]

[Borodog]

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Wouldn't he need to know some estimate of the likelihood of each person getting any given question correctly? You could easily craft a test where this was 100:1 and a near lock to be cheating.

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Good point. The average on the test was 10.3/19, with a standard deviation of 3.6. None of the questions were "gimmes." There were several other students that took the makeup, at the same time, at the same table, and their tests looked completely different. 2 students scored 8s, but their 8s were very different 8s, with little overlap between the questions they got wrong.

[Borodog]

Also remember, it's not just a matter of getting the same problems correct; it's also a matter of getting the incorrect problems incorrect in the same way.

[surftheiop]

Not that im going to guess on a percentage but 2 ?s (seeing as accusing someone of cheating in college is really serious).
Did they know each other well? If they did would studying together/in the same group be a feasible explanation for them making similar mistakes? Also on the ones they got wrong, did most of the class choose the same wrong answers if they got the problems in question wrong or were their wrong answers more unique? (This is based on my experience taking highschool tests when it seems most people whol get a question wrong do so for the same reason)

[Borodog]

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Not that im going to guess on a percentage but 2 ?s (seeing as accusing someone of cheating in college is really serious).
Did they know each other well? If they did would studying together/in the same group be a feasible explanation for them making similar mistakes?

[/ QUOTE ]

Could be, but they are in 2 different sections.

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Also on the ones they got wrong, did most of the class choose the same wrong answers

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No.

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if they got the problems in question wrong or were their wrong answers more unique? (This is based on my experience taking highschool tests when it seems most people whol get a question wrong do so for the same reason)

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[surftheiop]

Out of curiousity,
when skalansky comes in here and says they cheated with 99.9 percent certaintity what sort of action are you going to take?

[Shadowrun]

This is all coming from a current college student so take it as you will.

I think they are cheating 95% of the time. I do have a few questions for you.

1. Was the test the exact same version for both of them, or was their only 1 version of the exam?

2. Go to facebook.com make an account and look if they are friends (i would this for you, but i think you'd want to protect their privacy), also you do not need to be accepting as a "friend" by them to see who they are friends with.

3. If they are friends on facebook i think they are cheating 99.5%.

4. Even if you do not want to accuse them of cheating (out of lack of evidence) offer them each, or even the whole class some EC (i think as little as 1% would the job, and is likely to not change their grade) and ask them to the problems + show their work (questions should be using similiar principals to the ones used in this exam)

If the boy or the girl is totally unable to show their work, they likelyhood of cheating to me goes to 100%.

[jay_shark]

Don't you know if they're friends outside of class ? Do they usually sit or converse to each other ?

I also think the Facebook idea is a good one . Check to see if they're friends which will improve your case against them cheating on the exam .