Re: What does the p-value mean
- From: Peter Perkins <Peter.PerkinsRemoveThis@xxxxxxxxxxxxx>
- Date: Thu, 01 Dec 2005 17:52:39 -0500
Murphy O'Brien wrote:
If p<0.05 the probability of being right when you say "P is not Normal" is > 95%.
Well, not exactly. What I was trying to say was that the probability of incorrectly rejecting is a long-run property of the test procedure. It is not affected at all by a particular p-value. If, in a particular trial, your p-value is less than .05, then yes, your observed data fall in the rejection region, and that region has been defined to give the test procedure a 5% probability of false rejection. But that is not the same thing as what you said.
Some of this is angels on the head of a pin. If you reject the null when your p-value is less than .05, then you have a 5% probability of being wrong _if the null is indeed the truth_. That's a conditional probability, though, and you don't know in any particular case if the condition is true. I guess the 5% probability can also be thought of as a worst case unconditional probability too, so in that sense, the "> 95%" is correct.
- Peter .
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