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Lumifer comments on Against NHST - Less Wrong Discussion

57 Post author: gwern 21 December 2012 04:45AM

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Tags: psychology statistics frequentism

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Comment author: Tem42 25 November 2015 11:29:20PM 0 points [-]

Okay, stupid question :-/

“Almost all of them think it gives some direct information about how likely they are to be wrong, and that’s definitely not what a p-value does...”

But

"...the technical definition of a p-value — the probability of getting results at least as extreme as the ones you observed, given that the null hypothesis is correct..."

Aren't these basically the same? Can't you paraphrase them both as "the probability that you would get this result if your hypothesis was wrong"? Am I failing to understand what they mean by 'direct information'? Or am I being overly binary in assuming that the hypothesis and the null hypothesis as the only two possibilities?

Comment author: Lumifer 25 November 2015 11:53:36PM 2 points [-]

Aren't these basically the same?

Not at all. To quote Andrew Gelman,

The p-value is a strange nonlinear transformation of data that is only interpretable under the null hypothesis. Once you abandon the null (as we do when we observe something with a very low p-value), the p-value itself becomes irrelevant.

Also see more of Gelman on the same topic.

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