Quote:

Originally Posted by

**mcnarus**
*The 0% case can just as easily be explained by transposing the two versions in his mind and simply not re-checking. That is, say he listens to A and B and notes their differences. He then goes through the five randomized samples and does notice a difference each time... but consistently presses B when he meant A and vice versa because he transposed which version was which. That's not being a moron, that's just being mildly forgetful.*

If he did it once, yeah. But 5 times in a row? Come on.

You don't do if five times in a row -- you transpose A and B once and then use that transposition during the test. That's an extremely common thing to do. I was just doing hinge mortises the other day where I started out knowing that I had to set my jig for hinges but somehow early on switched that around in my head and instead set the jig for strike plates. I repeated this for all the hinges and it wasn't until I was done that I realized I had transposed the settings in my first step.

Quote:

Originally Posted by

**mcnarus**
*I maintain that neither 0% nor 100% can be easily explained by either good or bad guessing, since a 3% chance is too slim to use any kind of guessing as a pat answer. *

It's not a pat answer. It's a proper statistical inference. Black swans happen. Trying to rationalize them away is bad statistics. That's what you're guilty of here.

*Possible, but unlikely. It's FAR more possible that he really did detect a difference of some sort consistently and just transposed his choices.*

Really? What's the probability? We know the probability of bad guessing, and it's non-zero. You're just pulling a probability out of your nether reaches here.

Well, I guess we understand probability in different ways. I was always decent at math but I can't claim any high degrees specializing on that. If you have a mathematics degree, then I'd like to know what elementary error I'm making.

Because this does look elementary to me -- something you'd cover in Probability 101 in any college or advanced high school. A 3% chance means "unlikely" and "unlikely" means that even though, yes, black swans happen, any random swan is probably NOT black. If you're a betting man and the odds are only 3% that you're right, then your best bet is to fold.

Put one more way -- if I only have a 3% chance of consistently guessing a series of answers and I do consistently get the answers, then it's a fool's bet to say that I guessed -- probability theory says that I am far more likely to have known the answers than just guessed them.