I'd like to try out an explanation of something on you all: A p-value evaluates an argument that the data proves some claim, by applying the same argument to a fake model where we know the claim is false. The p-value is how often we would erroneously conclude it was true anyway.
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Replying to @DRMacIver
I am reasonably sure this is incorrect. See: http://rsos.royalsocietypublishing.org/content/1/3/140216 …
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Replying to @Meaningness
Hmm. I will read the paper, but I'm reasonably sure it's correct and is just a restatement of the definition of a p-value. Possibly there's some subtlety of interpretation here though.
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Replying to @DRMacIver
What is the “fake model where we know the claim is false”? this isn’t part of my (amateur) understanding.
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Replying to @Meaningness
The null hypothesis. e.g. if you want to say "the mean of these two populations is different" your null hypothesis might be that they are drawn from the same normal distribution, which is a fake model that you are testing the argument on.
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Replying to @DRMacIver
Ah. Well, I don’t think this is right: that’s not what the null hypothesis does, and you don’t generally know that the null hypothesis is false. But I’m not expert on this, so I will shut up now!
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Replying to @Meaningness
No I'm pretty sure it is, and that is what the null hypothesis does. Indeed you don't generally know that the null hypothesis is false (though it almost always is in the sense that all models are false), but the point is you can generate fake data conditional on it being true.
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OK! I’m officially shutting up now!
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