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Crash Course: Statistics
Example: Importance of Variable Dependency
07:10 - 09:12
A real life example of why the independence (or lack thereof) of multiple variables is important.
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Video Transcript
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be more likely.
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Fast forward to 2011, a student at the University of California, San Diego, Jonathan Dorfman,
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was accused of cheating on a midterm by his Chemistry professor.
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After two Academic Integrity Review Board hearings, Dorfman was expelled from UCSD,
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because he had a previous incident on his record.
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He then filed a lawsuit against the school.
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After the midterm, the professor had noticed that Dorfman had changed the Test Version
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on his answer sheet.
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There were four versions of the test -- A, B, C, and D. Students were told that if their
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test version wasn’t the same as the letter on their answer sheet, they should tell their
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test proctor.
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Dorfman HAD changed the letter on his answer sheet from D
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to A. But, he said that he arrived late, so he didn’t hear those instructions.
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He just saw that his test booklet had a different version than his answer sheet, and changed
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the answer sheet to match the test.
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After looking at all the exams, the professor also noticed that Dorfman’s test matched
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another student--they called them Student X--who had test version A, the same one Dorfman
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claimed to have.
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24 of the 26 answers matched between the two exams.
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8 of the 10 incorrectly answered questions, and all 16 of the correct ones.
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The professor of the class took this as further proof that Dorfman was cheating, and even
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went as far as to get a statistician to say that the probability of those same eight wrong
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answers happening by chance was a billion to one.
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Though the court documents do not reveal the exact math that the statistician used, it
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seems possible that they, like Dr. Meadow in Sally Clark’s case, probably assumed
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independence when no such assumption should be made.
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The wrong answers that students choose aren’t always totally random.
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On multiple choice tests, many times there’s one answer that looks good, even if it’s
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slightly inaccurate.
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And since these students were all taking the same course, and reading the same textbook,
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their incorrect answers aren’t independent of each other.
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Their misconceptions of the material were VERY likely to be dependent on their learning
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environment and therefore related.
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Dorfman’s lawyer displayed this, during the second review board hearing, by showing
