Campus: CSU Sacramento -- November 29, 2004
Prof Targets Student Cheats With Statistical Savvy
Final exams are just around the corner at universities nationwide, and with
them the ever-present challenge of student cheating. But this year, a professor
at California State University, Sacramento has prepared a new device to assist
Robert G. Mogull, who teaches business statistics, has shown that it takes only
a modest amount of effort to thwart cheating students. He has created a simple
statistical tool that any instructor can use to detect cheating on multiple-choice
His technique was published in an article that appeared in the September 2004
issue of the Journal of College Teaching and Learning titled "A Device to Detect
Student Cheating." It involves computing the likelihood of more than one student
missing the same test question - the easier the test question that students jointly
miss, the more likely they cheated. (A brief description of the method appears
"This is really a device to confirm an instructor's suspicions. That's what it's
best for," Mogull says. "Of course, I've learned over the years that students are
exceptionally clever at cheating. They can defeat any method of detection that we
can come up with. If they are really determined to cheat, they are better at it
than we are at stopping them."
Mogull was inspired by a recent real-life classroom teaching experience, in which
two of his students missed the same 26 questions out of a total of 100 questions
over four different exams. That got the statistician's heart pumping - but not
because he was angry.
"It was clear in my mind that they had cheated. That wasn't the question," Mogull
says. "I was mainly intrigued. When I saw their test scores and their identically
missed questions, I wanted to calculate the probability of it happening at random.
The ideas for the study just sort of exploded in my mind and it became one of the
easiest papers that I've ever written." He computed the chance of two students
missing the same 26 questions to be roughly 0.000000000000000004 percent. As for
the two students, he gave both of them a failing grade for the course.
Mogull, who believes cheating is much more common than most professors will
acknowledge or even recognize, does not plan to employ his cheat-detecting device
broadly. He says that even though it's very easy to apply, it's too time consuming
to use all the time. He says that the best procedure to reduce student copying is
to use different test versions simultaneously so that students can't share answers
with others sitting next to them.
Mogull's method, in short: After grading the Scantron forms and conducting an
Item Analysis, you have the probability that a student missed each test question.
To calculate the likelihood that two students would jointly miss the same question,
you square the probability of missing the particular question. Follow that
procedure for each identically missed question. Then multiply all the probabilities,
subtract from one, and you have the probability that the students collaborated.
Stated another way, subtract the percentage chance that they didn't cheat from 100
percent and you have the probability that they did cheat. The paper also offers
an option for finding the chance that two (or more) students would miss the same
question and also mark the same wrong answer.
The full article is available as a link from this press release at
www.csus.edu/news. Robert Mogull may be
contacted at (916) 278-7142 or at email@example.com.
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