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Reverse isn't the right word here, either. Better to restate the definition: the p-value is the probability of observing the data (as represented by its aggrega
by xapata 9y ago
Reverse isn't the right word here, either. Better to restate the definition: the p-value is the probability of observing the data (as represented by its aggregate statistics), under the condition of the null hypothesis.
- gwern 9y agoI say 'reverse' because that's what it is formally: confusing P(data|null) with P(null|data). It reverses the conditional probability.
- xapata 9y agoReversing the arguments of the conditional probability, yes, but just saying "it's the reverse" is a bit ambiguous. > If it is less than 5% probable that the null hypothesis is correct given our data, we will reject the null hypothesis and consider our alternate hypothesis (HA) to be correct. You could be reversing the 5% to 95%, could be reversing null hypothesis to alternate hypothesis, could be reversing reject to accept, etc. Too many moving parts. P-values are so often misinterpreted, it's best to err on the side of specificity.