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In Reply to: RE: statistics question posted by andy19191 on June 25, 2009 at 13:23:46
"""This is not correct. The procedure you describe is to test the hypothesis that you can tell the difference between your interconnects to a given level of confidence. Failing this test does not mean you cannot sometimes tell the interconnects apart. It means that you cannot reliably tell the interconnects apart."""
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.
Guessing right 80% of the time, over a large number of trials, is in fact strong evidence that my perception is influenced by the sound of the cables. It may also be influenced by what I had for lunch, or what random thoughts are going through my brain. But it is very likely influenced by the difference in sound---hence evidence that I can tell them apart (i.e. that their sound influences my perception).
"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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