Timeline for Estimate rate of real correct/wrong from 4 answers quiz.
Current License: CC BY-SA 2.5
16 events
| when toggle format | what | by | license | comment | |
|---|---|---|---|---|---|
| Apr 5, 2010 at 22:35 | answer | added | Buzz | timeline score: 1 | |
| Apr 1, 2010 at 17:15 | comment | added | Mark Meckes | I'll just make the observation that statisticians (who are a distinct breed from mathematicians; I'm not sure I've seen any here) are the people who would already have thought about this and may even know standard references that deal with exactly this kind of problem. | |
| Apr 1, 2010 at 17:00 | answer | added | Sune Jakobsen | timeline score: 2 | |
| Apr 1, 2010 at 14:21 | comment | added | Stefano Borini | @gowers : that is what I thought as well, but I guess this is not an unknown situation, and I assume there's a formalism to deal with these cases given also the result from the additional experiment. | |
| Apr 1, 2010 at 13:49 | comment | added | gowers | Without some extra information or hypothesis, the evidence is consistent with everyone who answered "Buzz Lightyear" genuinely believing that, and also consistent with everybody making the "Buzz Aldrin" confusion. But it sounds as though you have some prior distribution in mind, which tells you that if someone answers "Buzz Lightyear" then the probability that they think the answer is a character in Toy Story is almost zero. I don't think you can do without that, so if you really want to understand this example you may need to supplement it with another experiment. | |
| Mar 31, 2010 at 16:19 | comment | added | Kevin O'Bryant | Let $p_1,p_2,p_3,p_4$ be the proportion of students giving each answer. If the students were in two categories (knows, guesses uniformly), then $p_2-(p_1+p_3+p_4)/3$ is the proportion of students who are in category "knows". At least, as the number of students goes to infinity, with probability 1. If you want a confidence interval, you've got a little more work ahead of you. | |
| Mar 31, 2010 at 11:54 | comment | added | rgrig | Maybe a better model would be one in which each student picks an answer according to some probabilities p1, p2, p3, and p4. Those that 'know' the answer are simply those for which p2=1 and the others are 0. | |
| Mar 31, 2010 at 9:10 | comment | added | Stefano Borini | @Kevin : you are better than a RNG :) | |
| Mar 31, 2010 at 6:48 | comment | added | Kevin Buzzard | @OP: Is it George Harrison? | |
| Mar 31, 2010 at 3:15 | comment | added | Stefano Borini | @Tony : yep, that's an additional factor to keep into account. | |
| Mar 31, 2010 at 3:10 | comment | added | Tony Huynh | Of course there is a refinement of 3., where people can narrow the correct answer down to say 2 choices and then guess randomly. Somehow we want to distinguish these people from the truly clueless people. | |
| Mar 31, 2010 at 2:57 | comment | added | Steve Huntsman | Possibly of interest: en.wikipedia.org/wiki/Dempster%E2%80%93Shafer_theory | |
| Mar 31, 2010 at 2:11 | comment | added | Stefano Borini | @Joel : interesting point. changed. | |
| Mar 31, 2010 at 1:58 | history | edited | Stefano Borini | CC BY-SA 2.5 |
added 13 characters in body
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| Mar 31, 2010 at 1:54 | comment | added | Joel David Hamkins | Most philosophers would say that one can only `know' true things (or at least this is a highly standard position), and so you may want to adjust your terminology in item 2. It sounds peculiar to speak of people knowing an incorrect answer. | |
| Mar 31, 2010 at 1:39 | history | asked | Stefano Borini | CC BY-SA 2.5 |