Probability Question for David Sklansky

[PairTheBoard]

I would question the students and go for a confession. Give them a plea bargain. If they confess let them retake the test with both getting the lowest score between them on the retake - or maybe with points taken off their own score. Tell them if they don't confess you consider the evidence strong for cheating and you will have to take the matter to higher authorities. Opening it up for class discussion might be one such higher authority. You can also take into consideration your read on whether they are lying if they refuse to confess.

As for the strength of the evidence for cheating, you could argue that even assuming they both knew the answers to the same 14 questions - which is a longshot already - the chance that they would randomly guess the same way among the 4 incorrect choices on the 4 questions they both missed is 1 in 256. Without thinking about it too much that looks like about 99.6% confidence that the wrong guesses were copied by one of them.

PairTheBoard

[PairTheBoard]

btw, there are Statistics Experts here who could probably give you a more rigorous statistical inference than my 1 chance in 256. However, I don't think Sklansky is one of them. He's much better at computing odds on God.

PairTheBoard

[arahant]

wow. why are you even asking?
It's greater than 99.9% unless this was a really weird test.
I can't even see where their answers differ.

However, don't discount the possibility that only one was cheating by watching the other (presumably the worse student). This is actually more likely, imho, despite my basic assumption that cute girls are smart, chaste, and pure.

[Wyman]

[ QUOTE ]
btw, there are Statistics Experts here who could probably give you a more rigorous statistical inference than my 1 chance in 256. However, I don't think Sklansky is one of them. He's much better at computing odds on God.

PairTheBoard

[/ QUOTE ]

Zing!

I'd expect that they could dismiss some wrong answers, and thus there would be a higher probability (than 1/256) that they randomly guess the same wrong answers.

I have a facebook account, and I gave a quiz once and suspected cheating. I looked on facebook, and one of their "status updates" was "[Name] is a cheater."

I love the guilty conscience. The student had dropped before the next class.

FWIW, I agree with confronting them. Tell them your job is not to accuse them of or judge them for cheating. Your job is to take any situation which has overwhelming evidence of cheating and present it to the appropriate higher-ups. This way you come off as the coach/helper/advocate, rather than the complete adversary (as much as this is possible). Alternately, I've also simply said to the class: "There was clear evidence of cheating on this quiz/exam. I will be presenting these cases to the [honor council, dean, dept chair, or whatever-the-heck you have]. If you'd like to fess up before-hand, we can possibly work something out."

Seems to work.

[T50_Omaha8]

This is extremely, extremely unlikely making only one assumption: the questions they miss are random.

Let's say she walked in destined to miss 4 and he walked in destined to miss 5. What's the probability that he magically missed all 4 of the ones she missed?

There are 15 ways he can do this--by missing the 4 she missed and any other random problem. There are, of course, 19c5 ways he can miss 5 problems. That leaves a 15/11,628 or very close to a 1/800 chance that he misses the same 4 problems she did. This does not take into account that they guessed the exact same answer on each problem.

Some trains of thought will undermine this probability: students may have been more likely to miss those problems, for example. But the untrained eye tends to vastly overestimate the likelihood of this type of anomaly occuring by random chance. If you confront them, make sure you back it up with some of our arguments.

I say you make both of them take it again unannounced, switch up the question and answer order, and check the results. It is likely that one of them will have a very similar outcome and the other will score much more poorly.

[doucy]

need pics of girl to make an accurate estimate

[Phil153]

If you're going to do an odds analysis, one thing to consider is how many exams you've administered. For example, I got a royal flush the other day. You also have to adjust for the fact that they may have studied together, and easy to answer questions, which means that the 19C5 number is way too higher.

I'd say 90%. BTW, is it policy at your uni to allow people to sit together during exams? We always had rules like 2 table spacing, multiple exams for people seated together, etc.

[yukoncpa]

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You also have to adjust for the fact that they may have studied together,

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Yeah, this is what I was thinking of. I studied with hot chicks as often as possible.

[durrrr]

post the questions(all of them if possible)... also any other spots where one/both erased anything?

atm i'd say ~60-70%

edit: what class etc.

[durrrr]

[ QUOTE ]
[ QUOTE ]
You also have to adjust for the fact that they may have studied together,

[/ QUOTE ]

Yeah, this is what I was thinking of. I studied with hot chicks as often as possible.

[/ QUOTE ]

agreed, also the questions could just be off a bit. The fact that they had a different answer where the girl (who does worse usually) was wrong, makes it FARRR less likely imo they are cheating than if this wasn't there. W/o this info id say ~90-92%