> I didn't say the 5 gives you 4ish bits of information. I said it gives you 1.4 bits of information. Which is obviously wrong. The self-selection does provide

> I didn't say the 5 gives you 4ish bits of information. I said it gives you 1.4 bits of information. Which is obviously wrong. The self-selection does provide a lot of information. Students who believe themselves unlikely to score well are unlikely to take the test, which is why so many students get a 5.