As someone who works with data I can tell you that distributions can take on all kinds of unexpected shapes, especially when n=600. I think he's bluffing - the stats can't prove that anyone has cheated. That said, the deal he offered sounded pretty good when compared to the alternative.
I, as a non-statistician, agree that he was bluffing. If I were a student in that class with a high grade, cheating or no (because even the innocent may get accused and face the ostensibly severe consequences), I would be thinking "Hmm... Now how exactly does he plan on proving that I cheated?" Without a confession or third party who could reliably state that they know hypothetical-I was cheating, the possibility of actually proving misconduct on an individual level seems extremely remote.
I would love to hear some statistics folks weigh in on this. Or: speculation ftw!
My thoughts exactly. If I were a non-cheating student in that class, I would be very tempted to confess anyway, out of fear that I would be a victim of the prof's over-confidence in his statistical analysis. He mentioned being able to supply the dean with a list of people with 95% confidence that everyone who cheated was on the list, with no apparent concern for any false positives. The confession offer is pretty good in comparison.
"He mentioned being able to supply the dean with a list of people with 95% confidence that everyone who cheated was on the list, with no apparent concern for any false positives."
Right after that, he said that he couldn't be sure everyone on the list had cheated. He is saying that he thinks every cheater is on the list, but not everyone on the list is a cheater.
That assumes that proof of anything is required. That's not usually how college disciplinary actions work.
At its worst, universities will sometimes assume a student accused of wrongdoing is lying, and punish the student based solely on the word of the faculty/staff bringing the charge. This happens in lesser cases where the administration thinks it can get away with it, and when the student is frightened of harsher sanctions that might be inflicted if the student asserts his or her rights and demands a full hearing process.
At its best (typically in more serious cases), the disciplinary process resembles a civil case (except instead of a jury, it's more of a tribunal) where the required proof is a preponderance of the evidence.
It's no wonder 200 students confessed. If I was in that class and I'd never seen the test bank, I'd have confessed too. It's been my observation that the disciplinary process is better at railroading not-provably-guilty students than punishing provably-guilty students. I would not want to take my chances.
