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Re: No!

All results apply to the particular test and each test always has an hypothesis, but the results of a test verifying the hypothesis are generalisable while the results of a test which doesn't verify the hypothesis aren't generalisable.

What you actually test is the counter hypothesis which is the opposite of the hypothesis. So, if you're testing for audible differences between two cables and your hypothesis is that audible differences do exist, the counter hypothesis is "there are no audible differences between the cables". The only way you can fail to show the counter hypothesis is by actually showing there is an audible difference. So failing to verify the counter hypothesis is conclusive and verifies the hypothesis that there is a difference. If you end up with a result which fails to falsify the counter hypothesis, you're left wondering whether the failure was due to there being no audible difference or being due to the fact that the test wasn't capable of demonstrating the existence of a difference that was there.

Remember the requirements for repeatability and the assumption that nature acts consistently. If the counter hypothesis fails and there is only one way it can fail, then you can expect all future tests to return the same result. That's why failing to verify the counter hypothesis would confirm the hypothesis and demonstrate the existence of an audible difference. It's also why you can generalise from that outcome - it can only occur if the hypothesis is true.

On the other hand, if you can't falsify the counter hypothesis, you're always left with 2 options for why you failed and you can't eliminate either one of those options. It's something like trying to show that there are different things on the 2 sides to a coin by tossing it - the fact that it always comes up "heads" in a series of tosses doesn't demonstrate that there is no "tail" side, no matter how long the run of heads goes on for. You may have a two headed penny or you could just have "lucked into" a very long run of heads and you can never resolve which one it is by continuing to toss the coin because you haven't shown that the coin has 2 heads and it must always remain possible that it could come up "tails" on the next toss, just as it's always possible in principle that the test could verify the hypothesis if you ran it another time. It's the inability to eliminate this possibility of a positive result that prevents you from generalising from the outcome here.

There are ways of disproving some things, but it isn't by observation. You have to demonstrate that it's impossible in principle for the thing to occur because it's logically incompatible with the accepted theory. That still leaves open the possibility that the theory/accepted law is wrong but shifts the onus of proof so that anyone trying to prove the thing has to disprove the theory or, at the very least, prove that an exception to the theory exists.

David Aiken


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  • Re: No! - David Aiken 23:50:51 11/16/02 (0)


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