Had a similar thing come up a few years ago. And, this is how we did it: Each multiple choice (assuming 3 distractors, 1 correct answer) has a .33 probability of selecting the same wrong answer (assuming that all wrong answers are equally attractive, which can be shown by analyzing the wrong answer patterns of the other students on the items in question). Running the binomial probability of selecting the same 4 incorrect items out of 4 chances is p=.012. (.33^4)
That, combined with your regression idea should be fairly convincing evidence. Now, if it turns out that those wrong choices are more attractive you may have to do another approach, but it is doable. P (item 1) = .50 P (item 2) = .60 P (item 3) = .33 P (item 4) = .70 Multiply all those together and you get the probability of selecting the same 4 incorrect items out of 4 chances is p=.069. Not as convincing, but still not looking good for the student. I have a hard time believing the solid student didn't facilitate the poorer student's work, and therefore might be considered to blame, too. -- Paul Bernhardt Frostburg State University Frostburg, MD, USA On 12/17/09 4:00 PM, "John Kulig" <[email protected]> wrote: > > Yes, that time of year again! I have never used Turnitin.com but I want to > introduce another problem I just encountered ... > > Two students in stats both turned in an exam with the exact same multiple > choice answers(35 out of 39 correct, and both the correct AND incorrect > choices were identical). I have never seen this happen before. One student was > aceing the class and the other was on the verge of failing. I have a pretty > solid case of copying not just on this point on other parts of the exam > because the poorer student also had correct AND incorrect answers on the > computation part out to two decimal places (including a "proportion of > variance" effect size of 2.15 which is bogus), all without computation, just > answers written down. Because I am grading non-stop and need a diversion, I am > intrigued with guestimating the probability of the MC being identical on all > 39 given no cheating. It's obviously a low probability as my MC scores average > close to "optimal difficulty" level (in the 60 - 70% range), so it's not the > case that most people get most of them correct. > > Anybody ever try to model this problem? I can assume they both knew 35 > answers, get the frequencies of all the wrong answers for the class, and > assume people guess randomly when they don't know. But they only missed 4. I > can also regress this exam on previous exam scores and show that the poor > student getting only 4 wrong is an outlier, but that may not be convincing > enough .. and thoughts would be appreciated. > > If the student were brigher they should have changed a few answers and > scribbled a few computations here and there on the sheet! > > -------------------------- > John W. Kulig > Professor of Psychology > Plymouth State University > Plymouth NH 03264 > -------------------------- > > ----- Original Message ----- > From: "DeVolder Carol L" <[email protected]> > To: "Teaching in the Psychological Sciences (TIPS)" <[email protected]> > Sent: Thursday, December 17, 2009 2:56:53 PM GMT -05:00 US/Canada Eastern > Subject: [tips] It's that plagiarism time of year again... > > Hi, > I have a student who has done poorly on his exams but has turned in a > stunningly good paper. Frankly, I don't think he wrote it but I'm having > difficulty showing that. I have Googled key phrases but nothing has turned up, > so I don't think he copied and pasted, I think he bought it. Can anyone give > me some idea of what Turnitin.com charges for an individual license? It's the > only thing I can think of, other than confronting the student, which will most > likely be my next step. I hate this stuff, it takes so much time and really > takes a toll on my enthusiasm for grading. > > Thanks in advance for any help you can provide. > Carol > > > > > Carol DeVolder, Ph.D. > Professor of Psychology > Chair, Department of Psychology > St. Ambrose University > Davenport, Iowa 52803 > > phone: 563-333-6482 > e-mail: [email protected] > > > > > --- > To make changes to your subscription contact: > > Bill Southerly ([email protected]) > > --- > To make changes to your subscription contact: > > Bill Southerly ([email protected]) --- To make changes to your subscription contact: Bill Southerly ([email protected])
