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Warrigal comments on Case study: abuse of frequentist statistics - Less Wrong
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So I should have said "for the nine outcomes they considered, they all had at least 5% chance of happening"?
The p-value is the probability of getting a result "at least this extreme" given the null hypothesis, where "extreme" means "deviating from the null hypothesis", however that's defined. So, the test cut the outcome space into pieces, the most extreme of which had at least a 5% chance of happening.
I think.
... under the null hypothesis. I actually forgot this detail when replying to komponisto.