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In Reply to: RE: statistics question posted by mike1127 on June 25, 2009 at 13:56:10
"Well, that's not what my little primer on statistics says. There is a null hypothesis (H_0), alternative hypothesis, (H_1). If the sound of the cable has no influence on my perception, then the probability of guessing correctly is p=0.5. In other words, completely random. That's the null hypothesis. If we run 18 trials and I get 15 of them correct, then P=0.004. That means there was a 0.4% chance that p actually equals 0.5. There is a 99.6% chance that p is *something other than 0.5*. But the test cannot tell you what p is. Just that it's not 0.5."You mostly have it except for the meanings of the various probabilities.
p=0.5 ... that just means the probability of guessing correct on a single independent trial.
P=0.004 ... that just means the probability of getting 15 correct out of 18 trials due to chance alone.
And, as per my other (longer) post, the test does not involve rejecting small "p", that's just an attribute of the mathematical model associated with the null hypothesis, what we are really doing is comparing our result with what the model "says" about the likelyhood of such a value.
Everything matters, don't forget to tweak your placebos!
Edits: 06/25/09
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